Neumann Li-Yau gradient estimate under integral Ricci curvature bounds
| Autor: | Xavier Ramos Olivé |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Physics 58J32 (Primary) 58J35 (Secondary) Geometric analysis Applied Mathematics General Mathematics Regular polygon Boundary (topology) Differential Geometry (math.DG) Differential geometry FOS: Mathematics Neumann boundary condition Heat equation Mathematics::Differential Geometry Riemannian submanifold Ricci curvature Mathematical physics |
| Zdroj: | Proceedings of the American Mathematical Society. 147:411-426 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/14213 |
| Popis: | 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 ${\bf M}^n\subseteq {\bf N}^n$, satisfying the integral Ricci curvature assumption: \begin{equation} D^2 \sup_{x\in {\bf N}} \left( \oint_{B(x,D)} |Ric^-|^p dy \right)^{\frac{1}{p}} < K \end{equation} for $K(n,p)$ small enough, $p>n/2$, where $diam({\bf M})\leq D$. The boundary of ${\bf M}$ is not necessarily convex, but it needs to satisfy the interior rolling $R-$ball condition. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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