Local minimizers of the interface length functional: An approach via local paired calibrations

Abstract: We prove that partitions of open sets in the plane, whose network of interfaces consists of finitely many straight segments only meeting in triple points with angles of 120 degrees, locally minimize the interface area functional with respect to L^1 perturbations of the partition. To this end, we will introduce a localized version of so-called paired calibrations, which were proposed by Lawlor and Morgan, as well as Brakke, as a means of proving global minimality of partitions via constructing suitable vector fields. Our approach can also be viewed as a static version of gradient flow calibrations, by which we can prove weak-strong uniqueness results for mean curvature flow. This is joint work with Julian Fischer, Sebastian Hensel and Tim Laux.

mathematical physicsanalysis of PDEsclassical analysis and ODEscategory theorycomplex variablesfunctional analysislogicmetric geometryoptimization and control

Audience: researchers in the topic

VCU ALPS (Analysis, Logic, and Physics Seminar)

Series comments: Description: Research seminar on topics ranging from analysis and logic to mathematical physics.

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Meeting ID: 951 0562 0974

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