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Weighted Isoperimetric Inequalities in Warped Product Manifolds
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We prove some sharp isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We also relate them to inequalities involving the higher order mean-curvature integrals. Applications include some sharp eigenvalue estimates, P\'olya-Szeg\"o inequality, Faber-Krahn inequality, Sobolev inequality and some sharp geometric inequalities in some warped product spaces.
Title: Weighted Isoperimetric Inequalities in Warped Product Manifolds
Description:
We prove some sharp isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds.
We also relate them to inequalities involving the higher order mean-curvature integrals.
Applications include some sharp eigenvalue estimates, P\'olya-Szeg\"o inequality, Faber-Krahn inequality, Sobolev inequality and some sharp geometric inequalities in some warped product spaces.
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