On Stekloff eigenvalue problem

@article{Chen2000OnSE,
  title={On Stekloff eigenvalue problem},
  author={Roger R.-C. Chen and Chiung-Jue Anna Sung},
  journal={Pacific Journal of Mathematics},
  year={2000},
  volume={195},
  pages={277-296}
}
where q(x) is a C function defined on M, ∂νg is the normal derivative with respect to the unit outward normal vector on the boundary ∂M. In particular, when the boundary ∂M satisfies the “interior rolling R−ball” condition, we obtain a positive lower bound for the first nonzero eigenvalue in terms of n, the diameter of M , R, the lower bound of the Ricci curvature, the lower bound of the second fundamental form elements, and the tangential derivatives of the second fundamental form elements. 

Gradient estimates for some evolution equations on complete smooth metric measure spaces

In this paper, we consider the following general evolution equation $$ u_t=\Delta_fu+au\log^\alpha u+bu $$ on smooth metric measure spaces $(M^n, g, e^{-f}dv)$. We give a local gradient estimate of

Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces

Given a complete, smooth metric measure space $$(M,g,e^{-f}dv)$$(M,g,e-fdv) with the Bakry–Émery Ricci curvature bounded from below, various gradient estimates for solutions of the following general

Gradient estimates for some f-heat equations driven by Lichnerowicz’s equation on complete smooth metric measure spaces

Given a complete, smooth metric measure space (M,g,e-fdv)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}

References

SHOWING 1-10 OF 22 REFERENCES

On the parabolic kernel of the Schrödinger operator

Etude des equations paraboliques du type (Δ−q/x,t)−∂/∂t)u(x,t)=0 sur une variete riemannienne generale. Introduction. Estimations de gradients. Inegalites de Harnack. Majorations et minorations des

Neumann eigenvalue estimate on a compact Riemannian manifold

In their article, P. Li and S. T. Yau give a lower bound of the first Neumann eigenvalue in terms of geometrical invariants for a compact Riemannian manifold with convex boundary. The purpose of this

Applications of Eigenvalue Techniques to Geometry

Analysis has always been a powerful tool in the study of the geometry of manifolds. This fact has been reconfirmed by the recent developments in connection with the application of geometric analysis

The Geometry of the First Non-zero Stekloff Eigenvalue

Let (Mn, g) be a compact Riemannian manifold with boundary and dimensionn⩾2. In this paper we discuss the first non-zero eigenvalue problem \begin{align}\Delta\varphi & = & 0\qquad & on\quad M,\\

On Poincaré Type Inequalities

Using estimates of the heat kernel we prove a Poincare inequality for star-shape domains on a complete manifold. The method also gives a lower bound for the gap of the first two Neumann eigenvalues

Global heat kernel estimates

In this paper, by rst deriving a global version of gradient estimates, we obtain both upper and lower bound estimates for the heat kernel satisfying Neumann boundary conditions on a compact

A note on the isoperimetric constant

Reference EPFL-ARTICLE-161409 URL: http://archive.numdam.org/article/ASENS_1982_4_15_2_213_0.pdf Record created on 2010-12-03, modified on 2017-05-12