What is a Varifold? A biased introduction to Geometric Variational Problems
Institución: IM-UNAM
Tipo de Evento: Investigación
Cuándo |
12/11/2024 de 12:00 a 13:00 |
---|---|
Dónde | Auditorio "Alfonso Nápoles Gándara" |
Agregar evento al calendario |
vCal iCal |
Varifolds are a part of the basic language of many variational problems which involve geometric quantities (i.e., length, area, volume). This talk will provide a very biased introduction to this large class of fascinating problems. In particular, we will mainly discuss the history of one of the most famous examples: Plateau's problem, or the problem of minimal surfaces. The focus will be to provide an overview of the several successful frameworks in which Plateau's problem has been solved, emphasizing their strengths and weaknesses from the perspective of the Calculus of Variations and Geometric Measure Theory. This history provides the context to better understand how varifolds may be seen as the natural solution to the problems of the previous frameworks. If time permits, we will also discuss recent work in varifold regularity. There will be lots of pictures.