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Numerical approximation of curve evolutions in Riemannian manifolds

Nürnberg, Robert ; Garcke, Harald ; Barrett, John W


We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e. conformally equivalent to the Euclidean plane. Examples include the hyperbolic plane, the hyperbolic disc and the elliptic plane, as well as any conformal parameterization of a two-dimensional manifold in R-d, d >= 3. In these spaces we introduce stable numerical ...


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