Sponsored by
 
Events
News
 
[ Events ]
Seminars and Talks Conferences, Workshops and Special Events Courses and Lecture Series Taiwan Math. School
 

Activity Search
Sort out
Field
 
Year
Seminars  
 
NCTS Differential Geometry Seminar
 
20:00 - 21:00, November 27, 2024 (Wednesday)
Cisco Webex, Online seminar
(線上演講 Cisco Webex)
Dynamical Instability of Branched Singularities of Minimal Hypersurfaces
Salvatore Stuvard (University of Milan)

Abstract
The study of singularities of minimal surfaces is a fundamental problem in Geometric Analysis, which, for decades, has been fuelling some beautiful research in Differential Geometry, Geometric Measure Theory, Calculus of Variations, and PDE. It is widely known that a class of singularities which is particularly hard to treat is that of  “branched” or “flat” singularities: these cannot be detected at the classical blow-up / linearization level, because their tangent cones are smooth planes with multiplicity larger than one. Yet, flat singularities are unavoidable even in case of hypersurfaces, and even if stability is assumed. In this talk, I will prove, for minimal hypersurfaces, that if blow-ups at a flat singularity converge to the tangent plane at a suitable (mild) rate then the singularity is dynamically unstable, in the sense that it can be perturbed away with a non-trivial, area reducing mean curvature flow (in the sense of Brakke). The rate of convergence we need to assume is satisfied in all known examples, and it can be proved to hold for large classes of solutions. I will then argue that the mean curvature flow may be used as a selection principle for “well-behaved” solutions to Plateau’s problem, even possibly in the case of very wild boundaries. This is joint work with Yoshihiro Tonegawa (Institute of Science Tokyo).
 
Meeting number (access code): 2515 180 5783
Meeting password: P9HutGCZd34 
 
Organizers: Nicolau Sarquis Aiex (NTNU), Chung-Jun Tsai (NTU), Siao-Hao Guo (NTU)


 

back to list  
(C) 2021 National Center for Theoretical Sciences