Regularity of the Level Set Equation for Mean Curvature Flow with an Axis of Symmetry
Name
hance-jhance-phd-math-2023-thesis.pdf
Description
Thesis PDF
Size
353.52 KB
Format
Adobe PDF
Checksum (MD5)
dc83f9e61412ff1f9d743a125f0c00c5
Author(s)
Hance, Jackson R.
Advisor(s)
Colding, Tobias H.
Date Issued
September 2023
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis we study the regularity of viscosity solutions to the level set equation for mean curvature flow. We describe a set of hypotheses under which we can prove that the level sets of these solutions are C¹,¹ submanifolds of spacetime with well understood behavior near singular times. We then relate the derivatives of the solution of the level set flow to the solutions of certain evolution equations along fixed level sets. Finally we carry out this program to show that certain solutions with an axis of symmetry are in fact classical solutions of the level set problem.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
In Copyright - Educational Use Permitted
Copyright retained by author(s)
Persistent DSpace Link
