A Global Invariant of Conformal Mappings in Space
- 1 March 1973
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 38 (1) , 162-164
- https://doi.org/10.2307/2038790
Abstract
This paper shows that the total integral of the square of the mean curvature for a compact orientable surface in is an invariant of a conformal space mapping. This result is then used to answer a problem raised by T. Willmore and B.-Y. Chen concerning embeddings of compact orientable surfaces, and in particular tori, for which this integral is a minimum.Keywords
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