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

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Dysarthria

Constructing Isospectral Metrics via Principal Connectionsities; 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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Myocyte

An Adaptive Finite Element Method for Minimal Surfacesry time consuming, we derive an a posteriori controlled adaptive algorithm based on a recently developed and analyzed finite element method [11] [12] [13]. Numerical results are presented for two examples.

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Geometric Conditions on Free Boundariesoundary. 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 Generalized Mean Curvature Flow in Surface Processingh 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.

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https://doi.org/10.1007/978-3-642-55627-2Kolmogorov–Arnold–Moser theorem; differential equation; geometric analysis; nonlinear partial different