Stability of translating solutions to mean curvature flow

By Julie Clutterbuck, O. C. Schnürer, F. Schulze. 2005

208 citations recorded by the source corpus.

We prove stability of rotationally symmetric translating solutions to mean curvature flow. For initial data that converge spatially at infinity to such a soliton, we obtain convergence for large times to that soliton without imposing any decay rates.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/14096be70c0b39b08357e13d7e0ed4005890f3ee

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Stability of Euclidean space under Ricci flow (2007, background): “Clutterbuck and the first two authors proved stability of convex rotationally symmetric translating solutions to mean curvature flow in [3].”
Mean Curvature Flow in Higher Codimension: Introduction and Survey (2011, unknown): “Recently there has been done quite some work on the formation and classification of singularities in mean curvature flow [5,11,12,23, 25, 39, 47, 54, 56, 58, 59, 61, 71], partially motivated by Hamilton’s and Perelman’s [45, 66–68] work on the Ricci flow that in many ways behaves akin to the mean cu”
Translating solitons in Riemannian products (2018, background): “Now, proceeding as in [5] we denote u′ = φ and then (40) becomes φ′ = (1 + φ(2)) ( c− (n− 1) ′(r) ξ(r) φ ) =: F (r, φ(r)).”
Translating solitons of the mean curvature flow (2015, background): “Recently, in the subject has been paid considerable attention, see [4,8,16,18,19,23].”
Complete translating solitons to the mean curvature flow in ℝ3 with nonnegative mean curvature (2020, background): “There is as well a unique (up to horizontal translation) axisymmetric solution called the “bowl soliton” [1, 8] which has the asymptotic expansion as an entire graph u(x) = 1 2(n−1) |x| 2− log |x|+O(1).”
Uniqueness of the bowl soliton (2014, background): “The work [9] by Clutterbuck, Schnürer and Schulze also implicitly includes a uniqueness result under related assumptions.”