One-dimensional Projective Structures, Convex Curves and the Ovals of Benguria and Loss

Jacob Bernstein

Department of Mathematics, Johns Hopkins University, Baltimore, USA

Thomas Mettler

Department of Mathematics, ETH Zürich, Zürich, Switzerland

Date: August 26, 2014

Published Version: Comm. Math. Phys. 336 (2015), 933—952

1 Introduction
2 Preliminaries
3 Symmetries of the functionals
3.1 The Schwarzian derivative
3.2 Projective Symmetries
4 Deriving the geometric estimates
Appendix A On extending the conjecture of Benguria and Loss
Appendix B Projective structures
References