Allard Regularity Theory

  • Yoshihiro Tonegawa
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


Before we go into a full-fledged regularity theory for Brakke flows, it is certainly reasonable to consider a simpler time-independent situation. Suppose that we have a varifold V ∈Vk(U) which happens to be a time-independent Brakke flow as we defined in Sect.  2.2. This should mean that the normal velocity v is 0 and that v = h implies h = 0, which means that V is stationary. Let us adhere to the definition of the Brakke flow as in Definition  2.2 and check if this is indeed the case.


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© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Yoshihiro Tonegawa
    • 1
  1. 1.Tokyo Institute of TechnologyTokyoJapan

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