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math.FA2025
Affine isoperimetric inequalities for the first eigenvalue of the th order Affine -Laplace Operator
Dylan Langharst, Michael Roysdon
Recently, Haddad, Jiménez, and Montenegro introduced the affine -Laplace operator, , and studied associated affine versions of the isoperimetric inequalities for the first…
math.FA2025
Grünbaum's inequality for Gaussian and convex probability measures
Matthieu Fradelizi, Dylan Langharst, Jiaqian Liu +2
A celebrated result in convex geometry is Grünbaum's inequality, which quantifies how much volume of a convex body can be cut off by a hyperplane passing through its barycenter. In…
math.MG2025
On the polar of Schneider's difference body
Julián Haddad, Dylan Langharst, Galyna V. Livshyts +1
In 1970, Schneider introduced the th-order extension of the difference body of a convex body , the convex body in . He conject…