Keselman V.M. Euclidean isoperimetric inequality on non-compact riemannian manifold

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Keselman Vladimir Mikhailovich
 
Candidate of Physics and Mathematics, Associate Professor, Department of General and Applied Mathematics, Moscow State Industrial University
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Ulitca Avtozavodskaya, 16, 115280, Moscow, Russian Federation

Abstract. For arbitrary n-dimensional non-compact connected Riemannian manifold the isoperimetric function of the manifold can be reduced to Euclidean form (as in Rn) in the class of Riemannian metrics conformal to the initial metric of the manifold; moreover this form is asymptotically sharp.

Key words: Riemannian manifold, conformal type of manifold, conformal capacity, conformal metrics, isoperimetric function.

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Euclidean isoperimetric inequality on non-compact Riemannian manifold by Keselman V.M. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Science Journal of Volgograd State University. Mathematics. Physics. №2 (15) 2011 pp. 33-42

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