Convex Hulls of Orbits and Orientations of a Moving Protein Domain

TL;DR

This paper investigates the geometric structure of the convex hull of protein-related tensor orbits under rotations, providing insights into protein structure analysis in aqueous solutions.

Contribution

It characterizes the facial structure and Carathéodory number of convex hulls of rotation group orbits acting on symmetric tensors, linking geometry to protein structure.

Findings

Determined the facial structure of the convex hulls.

Analyzed the Carathéodory number for these convex hulls.

Applied geometric analysis to protein structure problems.

Abstract

We study the facial structure and Carath\'eodory number of the convex hull of an orbit of the group of rotations in R^3 acting on the space of pairs of anisotropic symmetric 3\times 3 tensors. This is motivated by the problem of determining the structure of some proteins in aqueous solution.