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Equality of the usual definitions of Brakke flow

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arxiv 1705.08789 v1 pith:SXJU6ERA submitted 2017-05-24 math.DG

Ananda Lahiri This is my paper · ORCID
classification math.DG
keywords brakkeflowmeasurecentralcorrectcurvaturedefinitiondefinitions
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In 1978 Brakke introduced the mean curvature flow in the setting of geometric measure theory. There exist multiple variants of the original definition. Here we prove that most of them are indeed equal. One central point is to correct the proof of Brakke's \S 3.5, where he develops an estimate for the evolution of the measure of time-dependent test functions.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Parabolic rectifiability of the Brakke flow

    math.DG 2026-06 unverdicted novelty 7.0 of 10

    Support of canonical space-time measure for Brakke flows is parabolic (k+2)-rectifiable, implying unique tangent flows and density agreement a.e., with equivalence of standard and space-time-Grassmann convergence.

  2. The space-time-Grassmann measure of the Brakke flow

    math.DG 2025-12 conditional novelty 7.0 of 10

    For every k-dimensional Brakke flow there is a canonical Radon measure on spacetime times the Grassmannian whose disintegrations characterize all equivalent classical flows.

  3. Gradient flow of phase transitions with fixed contact angle

    math.AP 2024-11 conditional novelty 6.0 of 10

    Under non-concentration assumptions, the singular limit of the Allen-Cahn flow with boundary contact energy is a varifold with a weak fixed contact angle, and the trace of the interior limit equals the limit of the bo...

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