Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow
Julin, V., & Niinikoski, J. (2023). Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow. Analysis and PDE, 16(3), 679-710. https://doi.org/10.2140/apde.2023.16.679
Published inAnalysis and PDE
DisciplineMatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköMathematicsAnalysis and Dynamics Research (Centre of Excellence)
© 2023 the Authors
We prove a new quantitative version of the Alexandrov theorem which states that if the mean curvature of a regular set in Rn+1 is close to a constant in the Ln sense, then the set is close to a union of disjoint balls with respect to the Hausdorff distance. This result is more general than the previous quantifications of the Alexandrov theorem, and using it we are able to show that in R2 and R3 a weak solution of the volume preserving mean curvature flow starting from a set of finite perimeter asymptotically convergences to a disjoint union of equisize balls, up to possible translations. Here by a weak solution we mean a flat flow, obtained via the minimizing movements scheme.
PublisherMathematical Sciences Publishers
Publication in research information system
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Related funder(s)Academy of Finland
Funding program(s)Research costs of Academy Research Fellow, AoF
Additional information about fundingThis research was supported by the Academy of Finland grant 314227.
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