Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Neumann Li-Yau gradient estimate under integral Ricci curvature bounds


Author: Xavier Ramos Olivé
Journal: Proc. Amer. Math. Soc. 147 (2019), 411-426
MSC (2010): Primary 58J32, 58J35
DOI: https://doi.org/10.1090/proc/14213
Published electronically: September 17, 2018
MathSciNet review: 3876759
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a Li-Yau gradient estimate for positive solutions to the heat equation, with Neumann boundary conditions, on a compact Riemannian submanifold with boundary $\textbf {M}^n\subseteq \textbf {N}^n$, satisfying the integral Ricci curvature assumption: \begin{equation} D^2 \sup _{x\in \textbf {N}} \left ( \oint _{B(x,D)} |Ric^-|^p dy \right )^{\frac {1}{p}} < K \end{equation} for $K(n,p)$ small enough, $p>n/2$, and $diam(\textbf {M})\leq D$. The boundary of $\textbf {M}$ is not necessarily convex, but it needs to satisfy the interior rolling $R-$ball condition.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 58J32, 58J35

Retrieve articles in all journals with MSC (2010): 58J32, 58J35


Additional Information

Xavier Ramos Olivé
Affiliation: Department of Mathematics, University of California, Riverside, Riverside, California 92521
ORCID: 0000-0003-3656-1822
Email: olive@math.ucr.edu

Keywords: Geometric analysis, differential geometry, Neumann heat kernel, integral Ricci curvature, Li-Yau gradient estimate
Received by editor(s): April 12, 2018
Received by editor(s) in revised form: April 25, 2018
Published electronically: September 17, 2018
Communicated by: Guofang Wei
Article copyright: © Copyright 2018 American Mathematical Society