In this paper we consider long time behavior of a mean curvature flow of nonparametric surface in ℝn, with respect to a conformal Riemannian metric. We impose zero boundary value, and we prove that the solution tends to 0 exponentially fast as t → ∞. Its normalization u/sup u tends to the first eigenfunction of the associated linearized problem
Long time behavior of Riemannian mean curvature flow of graphs / Citti, Giovanna; Manfredini, M. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 273:2(2002), pp. 353-369. [10.1016/S0022-247X(02)00233-0]
Long time behavior of Riemannian mean curvature flow of graphs
Manfredini M
2002
Abstract
In this paper we consider long time behavior of a mean curvature flow of nonparametric surface in ℝn, with respect to a conformal Riemannian metric. We impose zero boundary value, and we prove that the solution tends to 0 exponentially fast as t → ∞. Its normalization u/sup u tends to the first eigenfunction of the associated linearized problem
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