Abstract of Hessian Energy And Optimal Parametrisations Of Surfaces

Mathematics Research Report CMA-MRR75-94

Hessian Energy And Optimal Parametrisations Of Surfaces

Yi Fang and John E. Hutchinson

Abstract: Suppose $S\subset\Bbb R^n$ is a smooth surface with boundary, having the same topological type as the disc. We consider the problem of obtaining ``optimal'' parametrisations $Y : \overline{\Omega}\ (\subset\Bbb R^2)\rightarrow S$ where both $\Omega$ and $Y$ are arbitrary. We give a positive answer to various formulations of this problem, which we call the Cartography Problem. Some examples, related problems, and regularity results are also considered.

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