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Session

An: Analysis Location: D436 Session Chair: Lisa Beck Session Chair: Franz Gmeineder

Presentation 2

Volume-preserving continuous deformations into a ball with continuously decreasing surface area Marc Oliver Rieger, Olaf Post Universität Trier, Germany It is a classical result that sufficiently regular sets can be continuously deformed into a ball while simultaneously decreasing surface area. During this deformation, however, it is surprisingly difficult to ensure that the surface area changes continuously. We present a construction that guarantees the existence of such a deformations with continuously decreasing surface area. This result can be useful in certain constructions in the calculus of variations.