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Abstract We prove uniqueness of tangent cones for forced mean curvature flow, at both closed self-shrinkers and round cylindrical self-shrinkers, in any codimension. The corresponding results for mean curvature flow in Euclidean space were proven by Schulze and Colding–Minicozzi, respectively. We adapt their methods to handle the presence of the forcing term, which vanishes in the blow-up limit but complicates the analysis along the rescaled flow. Our results naturally include the case of mean curvature flows in Riemannian manifolds.
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Uniqueness of Regular Tangent Cones for Immersed Stable Hypersurfaces
Abstract We establish uniqueness and regularity results for tangent cones (at a point or at infinity), with isolated singularities arising from a given immersed stable minimal hypersurface with suitably small (non-immersed) singular set. In particular, our results allow the tangent cone to occur with any integer multiplicity.
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- Award ID(s):
- 2204301
- PAR ID:
- 10556322
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Archive for Rational Mechanics and Analysis
- Volume:
- 248
- Issue:
- 6
- ISSN:
- 0003-9527
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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