A Minkowski type inequality in space forms
Chao Xia
TL;DR
This paper proves an optimal Minkowski type inequality in space forms by applying a general Reilly formula to a Neumann boundary value problem, extending geometric inequalities in curved spaces.
Contribution
It introduces a novel application of the Reilly formula to establish a new Minkowski inequality in space forms.
Findings
Established an optimal Minkowski inequality in space forms.
Extended geometric inequality techniques to curved space settings.
Demonstrated the utility of the Reilly formula in boundary value problems.
Abstract
In this note we apply the general Reilly formula established in \cite{QX} to the solution of a Neumann boundary value problem to prove an optimal Minkowski type inequality in space forms.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Nonlinear Partial Differential Equations