Special Session 38: 

Finite time singularities of geometric evolution equations and a reverse isoperimetric inequality

Simon S Blatt
University Salzburg
Austria
Co-Author(s):    
Abstract:
The classification of singularities in both stationary as well as time dependent solutions of partial differential equations is and has been throughout the last decades in the centre of mathematical research. A natural question of course is, whether or not such singularities exist. In the talk I will first present some well-known results in this direction in the context of geometric evolution equations. We will then discuss some new results for the constrained Willmore flow and - time permitting - similar equations in the context of the M\obius energy. Parts of them rely on the fact that every sphere eversions has a quadruple point and a new reverse isoperimetric inequality. Our approach extends and simplifies results due to McCoy and Wheeler.