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Geometric Analysis Seminar

Nondegenerate minimal submanifolds as energy concentration sets

Alessandro Pigati - NYU

Location:  Hill Center Room 705
Date & time: Tuesday, 13 December 2022 at 2:50PM - 3:50PM

Abstract: Various energies of physical significance have been shown to effectively approximate the area functional, in codimension one and two.
These energies are defined on the set of functions on a given ambient manifold, and for critical maps they tend to concentrate towards a (possibly singular) minimal submanifold.
In this talk we answer the converse problem: we show that any nondegenerate minimal submanifold of the corresponding codimension does arise in this way.
The strategy is entirely variational and generalizes a recent work for geodesics (by Colinet, Jerrard, and Sternberg), by extending two key geometric measure theory results to arbitrary dimension.
(Joint work with Guido De Philippis)

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