Alvaro Pampano -- A New Variational Characterization of Invariant Constant Mean Curvature Surfaces
Author information
- Alvanro Pampano
- Texas Tech University
- Website: https://www.math.ttu.edu/~apampano/
Abstract:
Constant mean curvature (CMC) surfaces have played an important role in Differential Geometry and Mathematics since their origin in the eighteenth century. It is well-known that these surfaces arise as critical points of the area functional for variations preserving the enclosed volume. In this talk, we will introduce a new local variational characterization for CMC surfaces of Riemannian and Lorentzian 3-space forms, provided that they are invariant under rigid motions of the ambient space.
In this setting, all the information about the surface is encoded in the profile curve, which happens to be critical for a curvature depending energy that extends a functional studied by Blaschke.
In the second part of the talk, we will restrict our analysis to the round 3-sphere. Although our characterization is local in nature, we will show that it can also be used to obtain some global results. For instance, to check the Lawson’s conjecture.