About

Rick Rugang Ye is a professor in the Department of Mathematics at the University of California, Santa Barbara. His research interests include Differential Geometry, Geometric Analysis, the Ricci Flow, and the Geometrization of Lower Dimensional Manifolds, as well as Mathematical Physics. He has been actively involved in organizing seminars and conferences related to these fields, such as the Differential Geometry Seminar, AMS Special Sessions on Ricci Flow and Geometrical Analysis, and the Santa Barbara Summer Conference in Geometry. His teaching activities encompass a variety of mathematics courses, including advanced topics in geometry and analysis, as evidenced by his syllabus contributions for courses like Math 240B, Math 124B, and Math 117, among others.

Research topics

• Geometry
• Pure mathematics
• Mathematics
• Mathematical analysis
• Combinatorics

Selected publications

• Ricci Flow and Gromov Almost Flat Manifolds

  arXiv (Cornell University) · 2022

  Senior authorCorresponding
  • Mathematics
  • Pure mathematics
  • Combinatorics

  We employ the Ricci flow to derive a new theorem about Gromov almost flat manifolds, which generalizes and strengthens the celebrated Gromov--Ruh Theorem. In our theorem, the condition $diam^2 |K| \leq ε_n$ in the Gromov--Ruh Theorem is replaced by the substantially weaker condition $\|Rm\|_{n/2}$ $ C_S^2 \leq \varepsilon_n$.

  PublisherOA PDFDOI

• Ricci flow and a sphere theorem for L/2-pinched Yamabe metrics

  Advances in Mathematics · 2021

  Senior authorCorresponding
  • Mathematics
  • Mathematical analysis
  • Pure mathematics
  PublisherDOI

• The Logarithmic Sobolev and Sobolev Inequalities Along the Ricci Flow

  Communications in Mathematics and Statistics · 2015-03-01 · 31 citations

  article1st authorCorresponding
  PublisherDOI

• Sobolev Inequalities, Riesz Transforms, and the Ricci Flow

  Communications in Mathematics and Statistics · 2014-06-01 · 5 citations

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• A Note on Obata’s Rigidity Theorem

  Communications in Mathematics and Statistics · 2014-12-01 · 11 citations

  articleOpen accessSenior author
  PublisherOA PDFDOI

• A Note On Obata's Rigidity Theorem I

  arXiv (Cornell University) · 2012-03-23

  preprintOpen accessSenior author

  In this note we present various extensions of Obata's rigidity theorem concerning the Hessian of a function on a Riemannian manifold. They include general rigidity theorems for the generalized Obata equation, and hyperbolic and Euclidean analogs of Obata's theorem. Besides analyzing the full rigidity case we also characterize the geometry and topology of the underlying manifold in more general situations.

  PublisherOA PDFDOI

• Existence, Convergence and Limit Map of the Laplacian Flow

  ArXiv.org · 2009-12-01 · 17 citations

  preprintOpen accessSenior author

  We prove short time existence and uniqueness of the Laplacian flow starting at an arbitrary closed $G_2$-structure. We establish long time existence and convergence of the Laplacian flow starting near a torsion-free $G_2$-structure. We analyze the limit map of the Laplacian flow in relation to the moduli space of torsion-free $G_2$-structures. We also present a number of results which constitute a fairly complete algebraic and analytic basis for studying the Laplacian flow.

  PublisherOA PDFDOI

• A Neumann Type Maximum Principle for the Laplace Operator on Compact Riemannian Manifolds

  Journal of Geometric Analysis · 2009-04-02 · 3 citations

  articleSenior author
  PublisherDOI

• Curvature estimates for the Ricci flow I

  Calculus of Variations and Partial Differential Equations · 2008-01-10 · 15 citations

  article1st authorCorresponding
  PublisherDOI

• The logarithmic Sobolev inequality along the Ricci flow: the case $λ_0(g_0)=0$

  arXiv (Cornell University) · 2007-08-15

  preprintOpen access1st authorCorresponding

  We extend our previous results on the logarithmic Sobolev inequality along the Ricci flow in the case $λ_0(g_0)>0$ to the case $λ_0(g_0)=0$.

  PublisherDOI

Frequent coauthors

• Guofang Wei

  7 shared

• Guoqiang Wu

  Zhejiang Sci-Tech University

  2 shared

• Eric Chen

  2 shared

• Peter Petersen

  2 shared

• Xianzhe Dai

  2 shared

• Wei Ding

  Shanghai Jiao Tong University

  1 shared

• Kung-Ching Chang

  1 shared

• Feng Xu

  1 shared