Special Lecture: Brent Albrecht (UCSB), 'Optimal Mass Transport and Curvature Bounds'

Event Date: 

Tuesday, May 14, 2013 - 11:00am to 12:00pm

Event Location: 

  • 6635 South Hall

Event Contact: 

Brent Albreckt

Email: Brentalbreckt@math.ucsb.edu

Abstract: Transport maps arising on a complete connected Riemannian manifold satisfy an associated highly-nonlinear partial differential equation known as the Monge-Ampère equation. We discuss the concept of Hessian metrics --- one of the geometric tools implemented by Eugenio Calabi in his investigation of the properties of solutions of the general Monge-Ampère equation for the n-dimensional Euclidean space --- and give an exposition of the speaker's results concerning modified Hessian pseudo-metrics. Our results generalize a result of Calabi to n-dimensional space forms of constant positive sectional curvature and lead to new lower Ricci curvature bounds.