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Isoperimetric inequalities for wedge-like membranes and convex cones with Lotfi Hermi
This is a past event.
Friday, December 1, 2023 at 2:00pm to 3:00pm
DM - Deuxieme Maison, 164
11200 SW 8th ST, Deuxieme Maison, Miami, Florida 33199
Speaker. Lotfi Hermi, Math & Stats, FIU.
Title. Isoperimetric inequalities for wedge-like membranes and convex cones
Abstract. We use the weighted isoperimetric inequality of J. Ratzkin for a wedge domain in higher dimensions to prove new isoperimetric inequalities for weighted Lp-norms of the fundamental eigenfunction of a bounded domain in a convex cone-generalizing earlier work of Chiti, Kohler-Jobin, and Payne-Rayner. We also introduce relative torsional rigidity for such domains and prove a new Saint-Venant-type isoperimetric inequality for convex cones. Finally, we prove new inequalities relating the fundamental eigenvalue to the relative torsional rigidity of such a wedge domain thereby generalizing our earlier work to this higher dimensional setting and show how to obtain such inequalities using the Payne interpretation in Weinstein fractional space.
The problems have a history related to techniques developed by Alexandre Weinstein (1897 - 1979) in the context of fluid mechanics, and an old question first addressed by Lawrence E. Payne (1923 - 2011) and Hans Weinberger (1928 - 2017), working as postdocs under Weinstein in the 1950s.
Location: DM 164
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Meeting ID: 930 5388 4755