Speaker: Dr. Elisabeth Werner, Case Western Reserve University
Title: “The $L_p$-Floating Area, Entropy, and Isoperimetric Inequalities on the Sphere”
Abstract: The floating area was previously investigated as a natural extension of classical affine surface area to non-Euclidean convex bodies in spaces of constant positive curvature. We  introduce the family of $L_p$-floating areas for spherical convex bodies, as an analog to  $L_p$-affine surface area measures from Euclidean geometry. We investigate a duality formula, monotonicity and isoperimetric inequalities for this new family of curvature measures on spherical convex bodies. If time permits, we introduce a new entropy functional for spherical convex bodies using the \$L_p$-floating area, and a dual isoperimetric inequality is established. Based on joint works with Florian Besau.

The Analysis and Applied Mathematics (AAM) Seminar is intended for Kennesaw State faculty working in the various areas of analysis and applied mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone interested in attending.

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