Vincent Shaw
Kent State University
Title
On the Homothety Conjecture for the Body of Buoyancy in the Euclidean Plane
Abstract
We investigate a homothety conjecture for the body of buoyancy for convex bodies that are close the unit ball in the Euclidean plane. Let $K\subset\mathbb{R}^2$ be a convex body and fix $\delta\in(0,\pi/2)$. It is shown that there exists $\epsilon=\epsilon(\delta)>0$ such that if $(1-\epsilon)\mathbb{B}\subset K \subset (1+\epsilon)\mathbb{B}$ and the body of buoyancy of $K$ with respect to $\delta$ is homothetic to $K$, then $K$ must be an ellipse.
