Existence and Regularity Theories of Brakke Flow

Explore the intricacies of Brakke flow in this comprehensive lecture by Yoshihiro Tonegawa from Tokyo Institute of Technology. Delve into existence and regularity theories, beginning with an introduction to the topic and initial configuration. Examine unit tests and their significance in the study of Brakke flow. Investigate linear and alpha regularities, as well as dispersed irregularity. Gain insights into the Monotonicity Formula and its applications. Analyze the relationship between Brakke flow and minimal surfaces, with a focus on cylindrical configurations. This 75-minute talk, part of the International School on Extrinsic Curvature Flows, offers a deep dive into advanced mathematical concepts for researchers and students in the field.