Monotonicity theorems and how to compare them

Abstract: I will present two results. The first one concerns minimal surfaces of the hyperbolic space and is a relation between their renormalised area (in the sense of Graham and Witten) and the length of their ideal boundary measured in different metrics of the conformal infinity. The second result concerns minimal submanifolds of the sphere and is a relation between their volume and antipodal-ness. Both results were obtained from the same framework, which involves new monotonicity theorems and a comparison principle for them.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

[[Please provide your first and last name so that the speaker can identify you. Kindly submit your questions or comments using the chat box, not via audio.]]

The livestream is on Zoom at uqam.zoom.us/j/88383789249 It is recommended to subscribe to the CIRGET newsletter. Please send an email to haedrich.alexandra@uqam.ca , providing your name and affiliation.

Some talks can be seen at www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA