Huai-Dong Cao - Academia.edu (original) (raw)

Papers by Huai-Dong Cao

$Research paper thumbnail of Aronson-B\'enilan estimates for the fast diffusion equation under the Ricci flow$

arXiv (Cornell University), Jul 28, 2016

arXiv (Cornell University), Apr 3, 2023

arXiv (Cornell University), Apr 29, 1999

arXiv (Cornell University), Jun 23, 2020

arXiv (Cornell University), Mar 23, 2009

arXiv (Cornell University), Jan 15, 2015

One of the most eminent of contemporary mathematicians, Shing-Tung Yau has received numerous hono... more One of the most eminent of contemporary mathematicians, Shing-Tung Yau has received numerous honors, including the 1982 Fields Medal, considered the highest honor in mathematics, for his work in differential geometry. He is known also for his work in algebraic and Kahler geometry, general relativity, and string theory. His influence in the development and establishment of these areas of research has been great. These five volumes reproduce a comprehensive selection of his published mathematical papers of the years 1971 to 1991-a period of groundbreaking accomplishments in numerous disciplines including geometric analysis, Kahler geometry, and general relativity. The editors have organized the contents of this collection by subject area-metric geometry and minimal submanifolds; metric geometry and harmonic functions; eigenvalues and general relativity; and Kahler geometry. Also presented are expert commentaries on the subject matter, and personal reminiscences that shed light on the development of the ideas which appear in these papers.

$Research paper thumbnail of Aronson-B\'enilan estimates for the porous medium equation under the Ricci flow$

arXiv (Cornell University), Feb 28, 2014

arXiv (Cornell University), Jan 3, 2011

arXiv (Cornell University), Dec 8, 2014

$Research paper thumbnail of Linear stability of Perelman's <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ν</mi></mrow><annotation encoding="application/x-tex">\nu</annotation></semantics></math>ν-entropy on symmetric spaces of compact type$

arXiv (Cornell University), Apr 9, 2013

This volume includes papers presented by several speakers at the Geometry and Topology conference... more This volume includes papers presented by several speakers at the Geometry and Topology conferences at Harvard University in 2011 and at Lehigh University in 2012. Included are works by Simon Brendle, on the Lagrangian minimal surface equation and related problems; by Sergio Cecotti and Cumrun Vafa, concerning classification of complete N=2 supersymmetric theories in four dimensions; by F. Reese Harvey and H. Blaine Lawson Jr., on existence, uniqueness, and removable singularities for non-linear PDEs in geometry; by Janos Kollar, concerning links of complex analytic singularities; by Claude LeBrun, on Calabi energies of extremal toric surfaces; by Mu-Tao Wang, concerning mean curvature flows and isotopy problems; and by Steve Zelditch, on eigenfunctions and nodal sets.

Calculus of Variations and Partial Differential Equations

In this paper, we derive curvature estimates for 4-dimensional complete gradient expanding Ricci ... more In this paper, we derive curvature estimates for 4-dimensional complete gradient expanding Ricci solitons with nonnegative Ricci curvature (outside a compact set K). More precisely, we prove that the norm of the curvature tensor Rm and its covariant derivative ∇Rm can be bounded by the scalar curvature R by |Rm| ≤ CaRa and |∇Rm| ≤ CaRa (on M \K), for any 0 ≤ a < 1 and some constant Ca > 0. Moreover, if the scalar curvature has at most polynomial decay at infinity, then |Rm| ≤ CR (on M \K). As an application, it follows that that if a 4-dimensional complete gradient expanding Ricci soliton (M, g, f) has nonnegative Ricci curvature and finite asymptotic scalar curvature ratio then it has finite asymptotic curvature ratio, and C asymptotic cones at infinity (0 < α < 1) according to Chen-Deruelle [20].

The Journal of Geometric Analysis

Asian Journal of Mathematics, 2006