Evolving a convex closed curve to another one via a length-preserving linear flow |
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Authors: | Yu-Chu Lin |
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Institution: | Department of Mathematics, National Tsing Hua University, Hsinchu 30013, Taiwan |
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Abstract: | Motivated by a recent curvature flow introduced by Professor S.-T. Yau S.-T. Yau, Private communication on his “Curvature Difference Flow”, 2007], we use a simple curvature flow to evolve a convex closed curve to another one (under the assumption that both curves have the same length). We show that, under the evolution, the length is preserved and if the curvature is bounded above during the evolution, then an initial convex closed curve can be evolved to another given one. |
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Keywords: | 35K15 35K55 |
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