Generalized motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor

Hitoshi Ishii, Panagiotis Souganidis

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In this note we study the generalized motion of noncompact hypersurfaces with normal velocity depending on the normal direction and the curvature tensor. This work extends the by-now-classical works of Evans and Spruck (for mean curvature) and Chen, Giga and Goto (for general motions with sublinear curvature dependence), because it allows general dependence on the curvature tensor. It also allows a general treatment of the generalized evolution including noncompact hypersurfaces. A number of results regarding no interior, convexity, etc. are also presented.

Original languageEnglish
Pages (from-to)227-250
Number of pages24
JournalTohoku Mathematical Journal
Issue number2
Publication statusPublished - 1995
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)

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