Titlebook: Geometric Analysis and Nonlinear Partial Differential Equations; Stefan Hildebrandt,Hermann Karcher Book 2003 Springer-Verlag Berlin Heide

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On Karcher’s Twisted Saddle TowersProgress is usually judged by its achievements, and this also applies to mathematics. Therefore, the simplicity of a new idea is frequently well hidden under technical ballast which is necessary to press new results out of the idea.

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Singular Minimal SurfacesIn this survey I would like to report on some recent results concerning the ..for functions . : Ω → ℝ, Ω ⊂ ℝ. a domain, or Ω = ℝ.. Here α denotes some real number.

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A Finite Element Level Set Method for Anisotropic Mean Curvature Flow with Space Dependent WeightThe subject of this paper is the evolution of hypersurfaces Γ(.) ⊂ ℝ. according to the law

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Causes of Dysfunctional Cultureities; two manifolds are said to be isospectral if their spectra coincide. Spectral geometry deals with the mutual influences between the spectrum of a Riemannian manifold and its geometry. To which extent does the spectrum determine the geometry?

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Edwin Ordoukhanian,Azad M. Madnioundary. In smooth models approximating these free boundary problems, the geometric conditions are replaced by elliptic and parabolic equations. We describe the approximation of mean curvature flow by the Allen- Cahn equation, also with coupling, and of the Stefan problem with Gibbs-Thomson law by the quasi-stationary phase field equations.

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On the Nature of Disciplinary Intuitionsh field. They lead to interesting systems of nonlinear partial differential equations and allow the appropriate mathematical modeling of physical processes such as material interface propagation, fluid free boundary motion, crystal growth.