Journal
ANNALES DE L INSTITUT FOURIER
Volume 67, Issue 1, Pages 43-142Publisher
ANNALES INST FOURIER
DOI: 10.5802/aif.3077
Keywords
mean curvature flow; varifold; geometric measure theory
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Funding
- JSPS [25247008, 26220702]
- Grants-in-Aid for Scientific Research [26220702, 25247008] Funding Source: KAKEN
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Suppose that Gamma(0) subset of Rn+1 is a closed countably n-rectifiable set whose complement Rn+1\Gamma(0) consists of more than one connected component. Assume that the n-dimensional Hausdorff measure of Gamma(0) is finite or grows at most exponentially near infinity. Under these assumptions, we prove a global-in-time existence of mean curvature flow in the sense of Brakke starting from Gamma(0). There exists a finite family of open sets which move continuously with respect to the Lebesgue measure, and whose boundaries coincide with the space-time support of the mean curvature flow.
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