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Geometric Analysis Seminar

Uniqueness of blowups at isolated singularities for almost-area minimizers

Max Engelstein (MIT)

Location:  Hill 425
Date & time: Tuesday, 30 April 2019 at 2:00PM - 3:00PM

Abstract:  We prove a uniqueness of blowup result at isolated (multiplicity-one) singularities of (almost-)area minimizing currents. When the blowup has extra structure (i.e. integrability) we get a power rate of convergence.For minimizers, this reproves a result of Leon Simon (Annals, ’83) and similarly a key aspect of our proof is the Lojasiewicz inequality. However, our methods are purely variational, which allows us to study almost-minimizers (but prevents us from addressing stationary currents).

This is joint work with Luca Spolaor (MIT) and Bozhidar Velichkov (Universite Grenoble Alpes).

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