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Forced anisotropic mean curvature flow of graphs in relative geometry

Dieu Hung Hoang, Michal Beneš (2014)

Mathematica Bohemica

The paper is concerned with the graph formulation of forced anisotropic mean curvature flow in the context of the heteroepitaxial growth of quantum dots. The problem is generalized by including anisotropy by means of Finsler metrics. A semi-discrete numerical scheme based on the method of lines is presented. Computational results with various anisotropy settings are shown and discussed.

Geodesies on typical convex surfaces

Peter Manfred Gruber (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Using Baire categories uniqueness of geodesic segments and existence of closed geodesics on typical convex surfaces are investigated.

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