## Neumann Li-Yau gradient estimate under integral Ricci curvature bounds

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- by Xavier Ramos Olivé PDF
- Proc. Amer. Math. Soc.
**147**(2019), 411-426 Request permission

## 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

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## 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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 411-426 - MSC (2010): Primary 58J32, 58J35
- DOI: https://doi.org/10.1090/proc/14213
- MathSciNet review: 3876759