Minimizing the Squared Mean Curvature Integral for Surfaces in Space Forms
- 1 January 1992
- journal article
- research article
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 1 (3) , 191-207
- https://doi.org/10.1080/10586458.1992.10504258
Abstract
We minimize a discrete version of the squared mean curvature integral for polyhedral surfaces in three-space, using Brakke's Surface Evolver [Brakke 1992]. Our experimental results support the conjecture that the smooth minimizers exist for each genus and are stereographic projections of certain minimal surfaces in the three-sphere.Keywords
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