scholarly journals A maximum principle for mean-curvature type elliptic inequalities

2006 ◽  
pp. 389-398 ◽  
Author(s):  
James Serrin
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Curvature Type ◽  
Elliptic Inequalities

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Complete spacelike hypersurfaces in a Robertson–Walker spacetime

2011 ◽  
Vol 151 (2) ◽  
pp. 271-282 ◽  
Author(s):  
ALMA L. ALBUJER ◽  
FERNANDA E. C. CAMARGO ◽  
HENRIQUE F. DE LIMA
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Constant Mean Curvature ◽  
Rigidity Results ◽  
Complete Spacelike Hypersurfaces ◽  
Uniqueness Results ◽  
Spacelike Hypersurfaces ◽  
Generalized Maximum Principle ◽  
Non Parametric

AbstractIn this paper, as a suitable application of the well-known generalized maximum principle of Omori–Yau, we obtain uniqueness results concerning to complete spacelike hypersurfaces with constant mean curvature immersed in a Robertson–Walker (RW) spacetime. As an application of such uniqueness results for the case of vertical graphs in a RW spacetime, we also get non-parametric rigidity results.

scholarly journals Mean Curvature Type Flow with Perpendicular Neumann Boundary Condition inside a Convex Cone

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Fangcheng Guo ◽  
Guanghan Li ◽  
Chuanxi Wu
Keyword(s):  
Boundary Condition ◽  
Mean Curvature ◽  
Convex Cone ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Type Flow ◽  
Maximal Principle ◽  
Curvature Type

We investigate the evolution of hypersurfaces with perpendicular Neumann boundary condition under mean curvature type flow, where the boundary manifold is a convex cone. We find that the volume enclosed by the cone and the evolving hypersurface is invariant. By maximal principle, we prove that the solutions of this flow exist for all time and converge to some part of a sphere exponentially asttends to infinity.

Complete spacelike submanifolds in a locally symmetric semi-Riemannian space

2020 ◽  
Vol 31 (04) ◽  
pp. 2050033
Author(s):  
Shicheng Zhang ◽  
Yuntao Zhang
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Riemannian Space ◽  
Curvature Vector ◽  
Isoparametric Hypersurface ◽  
Mean Curvature Vector ◽  
Totally Umbilical ◽  
Type Formula ◽  
Spacelike Submanifolds ◽  
Generalized Maximum Principle

In this paper, complete spacelike submanifolds with parallel normalized mean curvature vector are investigated in semi-Riemannian space obeying some standard curvature conditions. In this setting, we obtain a suitable Simons type formula and apply it jointly with the well-known generalized maximum principle of Omori–Yau to show that it must be totally umbilical submanifold or isometric to an isoparametric hypersurface in a submanifold [Formula: see text] of [Formula: see text].

Global Gradient Estimate of the Mean Curvature Type Equation

2021 ◽  
Vol 11 (06) ◽  
pp. 1130-1136
Author(s):  
玉苏普 阿迪莱•
Keyword(s):  
Mean Curvature ◽  
Type Equation ◽  
Gradient Estimate ◽  
The Mean ◽  
Curvature Type
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