An isoperimetric comparison theorem
نویسندگان
چکیده
منابع مشابه
An Isoperimetric Comparison Theorem for Schwarzschild Space and Other Manifolds
We give a very general isoperimetric comparison theorem which, as an important special case, gives hypotheses under which the spherically symmetric (n− 1)-spheres of a spherically symmetric n-manifold are isoperimetric hypersurfaces, meaning that they minimize (n − 1)-dimensional area among hypersurfaces enclosing the same n-volume. This result greatly generalizes the result of Bray (Ph.D. thes...
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§0 Introduction §1 First and Second Variational Formulas for Area §2 Bishop Comparison Theorem §3 Bochner-Weitzenböck Formulas §4 Laplacian Comparison Theorem §5 Poincaré Inequality and the First Eigenvalue §6 Gradient Estimate and Harnack Inequality §7 Mean Value Inequality §8 Reilly’s Formula and Applications §9 Isoperimetric Inequalities and Sobolev Inequalities §10 Lower Bounds of Isoperime...
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