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arXiv 1908.074412019-08-20math.DG

The curve shortening flow with density of a spherical curve in codimension two

Francisco Viñado-Lereu

发表信息：: This is a pre-print of an article published in Journal of Evolution Equations (2020)
DOI：: 10.1007/s00028-020-00620-y

英文摘要：

In the present paper we carry out a systematic study about the flow of a spherical curve by the mean curvature flow with density in a 3-dimensional rotationally symmetric space with density $(M^3_w,\:g_w,\:ξ)$ where the density $ξ$ decomposes as sum of a radial part $φ$ and an angular part $ψ$. We analyse how either the parabolicity or the hyperbolicity of $(M^3_w,\:g_w)$ condition the behaviour of the flow when the solution goes to infinity.

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