Gregory R. Chambers
Abstract
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We completely characterize isoperimetric regions in \mathbb R^n with density e^h , where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex Density Conjecture due to Kenneth Brakke.
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We completely characterize isoperimetric regions in \mathbb R^n with density e^h , where h is convex, smooth, and radially symmetric. In particular, balls around the origin constitute isoperimetric regions of any given volume, proving the Log-Convex Density Conjecture due to Kenneth Brakke.
Key concepts: Isoperimetric inequality, Conjecture, Regular polygon, Mathematics, Combinatorics, Mixed volume, Logarithmically convex function, Convex body