Sharp estimates on the first eigenvalue of the $$p$$p-Laplacian with negative Ricci lower bound
By A. Naber, Daniele Valtorta. 2012
71 citations recorded by the source corpus.
We complete the picture of sharp eigenvalue estimates for the $$p$$p-Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator $$\Delta _p$$Δp when the Ricci curvature is bounded from below by a negative constant. We assume that the boundary of the manifold is convex, and put Neumann boundary conditions on it. The proof is based on a refined gradient comparison technique and a careful analysis of the underlying model spaces.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/338606697e4b122eab300006be8be14b5ae94390
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In Applied Mathematics
- Andrea Mondino
- Fabio Cavalletti
- Ben Andrews
- Nicola Gigli
- S. Brendle
- Emanuel Milman
- Luigi Ambrosio
- Robert Haslhofer
In Mathematical Physics
- Andrea Mondino
- Fabio Cavalletti
- Ben Andrews
- Guangxian Zhu
- Yiming Zhao
- Qi-Rui Li
- Shibing Chen
- Yong Huang
Citations in the corpus
- Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds (2015, methodology): “Actually, as explained in their paper, the arguments in [61] hold in the general case K ∈ R, N ∈ [1,∞), provided one identifies the correct model space.”
- Moduli of continuity, isoperimetric profiles, and multi-point estimates in geometric heat equations (2014, methodology): “[67] Aaron Naber and Daniele Valtorta, Sharp estimates on the first eigenvalue of the p-Laplacian with negative Ricci lower bound, Math.”