Reverse isoperimetric problems under curvature constraints

Series
Geometry Topology Seminar
Time
Friday, March 17, 2023 - 11:00am for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kateryna Tatarko – University of Waterloo – ktatarko@uwaterloo.cahttps://www.math.uwaterloo.ca/~ktatarko/
Organizer
Galyna Livshyts

Please Note: Note the unusual time!

In this talk we explore a class of λ-convex bodies, i.e., convex bodies with curvature at each point of their boundary bounded below by some λ>0. For such bodies, we solve two reverse isoperimetric problems.

In R3, we show that the intersection of two balls of radius 1/λ (a λ-convex lens) is the unique volume minimizer among all λ-convex bodies of given surface area.  We also show a reverse inradius inequality in arbitrary dimension which says that the λ-convex lens has the smallest inscribed ball among all λ-convex bodies of given surface area.

This is a joint work with Kostiantyn Drach.