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Mean Curvature Flow vs. Inverse Mean Curvature Flow
Student-Run Research Seminar| Speaker: | Brian Harvie, UC Davis |
| Related Webpage: | https://www.math.ucdavis.edu/~bharvie/ |
| Location: | Zoom |
| Start time: | Thu, Oct 1 2020, 1:10PM |
A geometric flow is a rule for deforming a surface through time according to its curvature at each point. A number of different flows naturally arise both as models for physical systems and as powerful tools for solving problems in geometry and topology. One (extrinsic) geometric flow called Mean Curvature Flow (MCF) causes a surface to contract through time, while another called Inverse Mean Curvature Flow (IMCF) causes a surface to expand. The analytic and geometric structure of MCF has been the subject of extensive study in recent decades, but far less is known about the structure of IMCF. Therefore, in this talk I will present some well-known properties of MCF and then introduce my own work on corresponding properties of IMCF, many of which provide a fascinating contrast. In particular, I will focus on the formation and characterization of singularities for both MCF and IMCF, as well as the closely-related problem of dynamical stability.
This will be an introductory talk, so in the interest of accessibility I will only include descriptions of major results rather than proofs of them.
Zoom: https://ucdavis.zoom.us/j/98164204505?pwd=cm50SmdL... pw: srrs2020
All grad students should have the password through the grad mailing list. Email krc@ucdavis.edu if you do not have access to this list and I will send you the password.