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List of works by Shing-Tung Yau

A Brief History of Kähler Geometry

scientific article published in 2015

A General Schwarz Lemma for Kahler Manifolds

scientific article published in 1978

A History in Sum

A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

scholarly article

A geometric approach to problems in birational geometry

scholarly article

A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

scientific article published in 1982

A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry

scientific article published in 1993

A realization of Thurston’s geometrization: discrete Ricci flow with surgery

scholarly article published in 2018

A remark on our paper “Negative holomorphic curvature and positive canonical bundle”

scientific article published in 2016

A simple proof of Bogomolov's Theorem on class $\nabla II_{0}$ surfaces with $b_{2} = 0^{1}$

scientific article published in 1990

A survey of Calabi-Yau manifolds

A survey of geometric structure in geometric analysis

scientific article published in 2011

Absolute phase-assisted three-dimensional data registration for a dual-camera structured light system

scientific article

Affine manifolds, SYZ geometry and the "Y" vertex

scientific article published in 2005

Autoequivalences of derived category of a K3 surface and monodromy transformations

scientific article published in 2004

Balanced metrics on non-Kähler Calabi-Yau threefolds

scientific article published in 2012

Brain surface conformal parameterization using Riemann surface structure

scientific article

Brain surface conformal parameterization with algebraic functions

scientific article published on 01 January 2006

Brain surface conformal parameterization with the Ricci flow

scientific article published on 15 September 2011

Brain surface conformal parameterization with the slit mapping

Brain surface parameterization using Riemann surface structure

article

Calabi's conjecture and some new results in algebraic geometry

scientific article (publication date: May 1977)

Calabi-Yau manifold

scientific article (publication date: 2009)

Calabi–Yau Volumes and Reflexive Polytopes

scientific article published in 2018

Canonical metrics on the moduli space of Riemann Surfaces I

scientific article published in 2004

Cohomology and Hodge Theory on Symplectic Manifolds: I

scientific article published in 2012

Cohomology and Hodge Theory on Symplectic Manifolds: II

scientific article published in 2012

Cohomology and Hodge theory on symplectic manifolds: III

scientific article published in 2016

Compact flat Riemannian manifolds

scientific article published in 1972

Compact manifolds of nonpositive curvature

scientific article published in 1972

Complete Kahler Manifolds With Nonpositive Curvature of Faster Than Quadratic Decay

scientific article published in 1977

Complete Kahler Manifolds with Zero Ricci Curvature. I

Complete Kähler manifolds with zero Ricci curvature II

Complete Kähler manifolds with zero Ricci curvature. I

scientific article published in 1990

Complete cscK Metrics on the Local Models of the Conifold Transition

scientific article published in 2015

Compression of surface registrations using Beltrami coefficients

Computational Conformal Geometry Behind Modern Technologies

scientific article published in 2020

Computing quasiconformal maps using an auxiliary metric and discrete curvature flow

Computing shortest words via shortest loops on hyperbolic surfaces

scientific article published in 2011

Conformal Slit Mapping and Its Applications to Brain Surface Parameterization

article

Curvature Preserving Diffeomorphisms

scientific article published in 1974

Curvature estimates for minimal hypersurfaces

article

D-type fiber-base duality

scholarly article

Davies–Gaffney–Grigor’yan Lemma on graphs

scientific article published in 2015

Detection of shape deformities using Yamabe flow and Beltrami coefficients

Differential equations from mirror symmetry

scientific article published in 1999

Differential equations on riemannian manifolds and their geometric applications

scientific article published in 1975

Differential zeros of period integrals and generalized hypergeometric functions

scholarly article

Eigenvalues of elliptic operators and geometric applications

scientific article published in 2004

Einstein manifolds with zero Ricci curvature

scientific article published in 2001

Embedded Minimal Surfaces, Exotic Spheres, and Manifolds with Positive Ricci Curvature

article

Erratum to: A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry

correction of a scholarly article

Erratum to: Optimization of Surface Registrations Using Beltrami Holomorphic Flow

scholarly article published in Journal of Scientific Computing

Evaluating quasi-local angular momentum and center-of-mass at null infinity

scientific article published in 2020

Evolution of Angular Momentum and Center of Mass at Null Infinity

scientific article published in 2021

Evolutionary dynamics on any population structure

scientific article

Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature

scientific article published in 1979

From special Lagrangian to Hermitian–Yang–Mills via Fourier–Mukai transform

GPU-assisted high-resolution, real-time 3-D shape measurement

scientific article published in October 2006

Gauss-Manin connection in disguise: Genus two curves

scientific article published in 2021

Generic nonsinusoidal phase error correction for three-dimensional shape measurement using a digital video projector

scientific article

Genus zero surface conformal mapping and its application to brain surface mapping

scientific article published in August 2004

Genus zero surface conformal mapping and its application to brain surface mapping.

scientific article published in July 2003

Global stability of spacetimes with supersymmetric compactifications

scientific article published in 2023

Graph Laplacians, Riemannian manifolds, and their machine-learning

scientific article published in 2022

Gravitational waves and their memory in general relativity

scientific article published in 2015

Harmonic functions on complete riemannian manifolds

scientific article published in 1975

Harmonic mappings and K�hler manifolds

scientific article published in 1983

Harmonic mappings and moduli spaces of Riemann surfaces

scientific article published in 2009

Harnack inequality for non-self-adjoint evolution equations

scientific article published in 1995

Hasse–Witt matrices, unit roots and period integrals

scientific article published in 2022

High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method

scientific article published on 01 April 2006

Higher eigenvalues and isoperimetric inequalities on Riemannian manifolds and graphs

scientific article published in 2000

Homotopically trivial symmetries of haken manifolds are toral

scientific article published in 1983

Hyperbolic Harmonic Mapping for Surface Registration

scientific article published on 12 May 2016

Hyperbolic harmonic brain surface registration with curvature-based landmark matching

scientific article published in January 2013

Independent component analysis-based classification of Alzheimer's disease MRI data

scientific article

Intrinsic brain surface conformal mapping using a variational method

Intrinsic measures of compact complex manifolds

scientific article published in 1975

Introduction to a deformed Hermitian Yang–Mills flow

scholarly article published in 2021

Invariant Solutions to the Strominger System on Complex Lie Groups and Their Quotients

scientific article published in 2015

Isoperimetric constants and the first eigenvalue of a compact riemannian manifold

scientific article published in 1975

K�hler-Einstein metrics on complex surfaces withC 1>0

scientific article published in 1987

Li-Yau inequality on graphs

scientific article published in 2015

Manifold fitting with CycleGAN

scholarly article

Mirror Principle I

scientific article published in 1999

Mirror Principle II

scientific article published in 1999

Mirror Principle. III

scientific article published in 2002

Mirror Principle. IV

Mirror of Atiyah flop in symplectic geometry and stability conditions

scholarly article

Mirror principle I

Mirror principle II

Mirror principle III

Mirror symmetry is T-duality

article published in 1996

Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction

scientific article published in January 2007

Negatively 1/4-pinched riemannian metric on a compact K�hler manifold

scientific article published in 1991

New results on the geometry of the moduli space of Riemann surfaces

scientific article published in 2008

Non-existence of continuous convex functions on certain Riemannian manifolds

scientific article published in 1974

Numerical Computation of Surface Conformal Mappings

scientific article published in 2012

Obstructions to the Existence of Sasaki–Einstein Metrics ⬇️

scholarly article

On sampling with Markov chains

article

On the Existence of Hermitian-Yang-Mills Connections in Stable Vector Bundles

scientific article published in 1986

On the Harnack inequalities of partial differential equations

scientific article published in 1994

On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold

scientific article published in 1981

On the Validity of the Definition of Angular Momentum in General Relativity

scientific article published in 2015

On the Willmore Conjecture for Surfaces

scientific article published in 2013

On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation

scholarly article by Shiu-Yuen Cheng & Shing-Tung Yau published July 1980 in Communications on Pure and Applied Mathematics

On the holonomic rank problem

scientific article published in 2014

On the path homology theory of digraphs and Eilenberg–Steenrod axioms

scholarly article published in 2018

On the proof of the positive mass conjecture in general relativity

scholarly article by Richard Schoen & Shing-Tung Yau published February 1979 in Communications in Mathematical Physics

On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I

article published in 1978

On the structure of manifolds with positive scalar curvature

scientific article published in 1979

On the sum of Ricci-curvatures for weighted graphs

scientific article published in 2021

Optimal mass transport for geometric modeling based on variational principles in convex geometry

scientific article published in 2014

Optimization of Surface Registrations Using Beltrami Holomorphic Flow

Particlelike solutions of the Einstein-Dirac equations

scientific article published in 1999

Path homology theory of multigraphs and quivers

scholarly article

Period integrals and tautological systems

scientific article published in 2017

Period integrals of vector bundle sections and tautological systems

scientific article published in 2021

Perspectives on geometric analysis

scientific article published in 2005

Poisson metrics on flat vector bundles over non-compact curves

scholarly article

Positive scalar curvature and minimal hypersurface singularities

scientific article published in 2019

Positivity of quasilocal mass

scientific article published on 10 June 2003

Positivity of the Total Mass of a General Space-Time

scientific article published in 1979

Proof That the Bondi Mass is Positive

scholarly article

Proof of the Positive-Action Conjecture in Quantum Relativity

scientific article published in 1979

Proof of the positive mass theorem. II

scientific article (publication date: March 1981)

Quantum statistics and spacetime topology: Quantum surgery formulas

scholarly article

Quasi-local energy with respect to a static spacetime

scholarly article

Quasi-local mass at axially symmetric null infinity

scientific article published in 2019

Quasi-local mass at null infinity in Bondi–Sachs coordinates ⬇️

scholarly article

Quasi-local mass in general relativity

scientific article published in 2010

Quasi-local mass near the singularity, the event horizon and the null infinity of black hole spacetimes

scientific article published on 28 September 2021

Quasilocal mass in general relativity

scientific article published on 15 January 2009

Recent development on the geometry of the Teichmüller and moduli spaces of Riemann surfaces

scientific article published in 2009

Reducing the Symmetric Matrix Eigenvalue Problem to Matrix Multiplications

scientific article published in 1993

Remarks on conformal transformations

scientific article published in 1973

Remarks on the group of isometries of a Riemannian manifold

scientific article published in 1977

Seiberg–Witten Differential via Primitive Forms

scholarly article

Shafarevich’s Conjecture for CY Manifolds I

scientific article published in 2005

Shape Analysis of Planar Multiply-Connected Objects Using Conformal Welding

scientific article published in July 2014

Shape analysis of vestibular systems in adolescent idiopathic scoliosis using geodesic spectra

scientific article published on 01 January 2010

Shape-Based Diffeomorphic Registration on Hippocampal Surfaces Using Beltrami Holomorphic Flow

scientific article published on 01 January 2010

Sharp Davies–Gaffney–Grigor’yan Lemma on graphs

scientific article published in 2017

Shiing-Shen Chern: as a great geometer of 20th century

scholarly article

Small resolutions of SU(5)-models in F-theory

Stable surfaces and free boundary marginally outer trapped surfaces

scientific article published in 2021

Stringy cosmic strings and noncompact Calabi-Yau manifolds

Surface parameterization using Riemann surface structure

article

Symplectic Conifold Transitions

scientific article published in 2002

Teichmüller Shape Space Theory and Its Application to Brain Morphometry

scientific article published on 01 January 2009

The Existence of Supersymmetric String Theory with Torsion

scientific article published in 2005

The Harnack estimate for the Ricci flow on a surface — revisited

scientific article published in 1997

The Past, Present and Future of Mathematics in China and India

scientific article published in 2013

The dynamical model for COVID-19 with asymptotic analysis and numerical implementations

scientific article published on 08 August 2020

The equivariant Dehn's lemma and loop theorem

scientific article published in 1981

The existence of embedded minimal surfaces and the problem of uniqueness

article

The theory of superstring with flux on non-Kähler manifolds and the complex Monge-Ampère equation

scientific article published in 2008

The topological uniqueness of complete minimal surfaces of finite topological type ⬇️

scholarly article

Topics on geometric analysis

scientific article published in 2012

Topology of Three Dimensional Manifolds and the Embedding Problems in Minimal Surface Theory

article

iSIRA: Integrated shift–invert residual Arnoldi method for graph Laplacian matrices from big data

scholarly article

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