As on arXiv
Abstract
In this paper we study the uniqueness of graphical mean curvature flow. We consider as initial conditions graphs of locally Lipschitz functions and prove that in the one dimensional case solutions are unique without any further assumptions. This result is then generalized for rotationally symmetric solutions. In the general - dimensional case, we prove uniqueness under additional conditions: we require a { \em uniform lower bound } on the second fundamental form and the height function of the initial condition. The latter result extends to initial conditions that are proper graphs over subdomains of .
Comments: Proposition 4.1 was eliminated and an assumption was added. The proof of Theorem 1.3 was updated accordingly
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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A Bernstein problem for translating solutions to the mean curvature flow
Topics Rotational symmetry & warped products, Stability & uniqueness · Shared terms “graphical”, “rotationally symmetric”
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Isotropy invariant graphical mean curvature flows in warped products
Topics Rotational symmetry & warped products · Shared terms “graphical mean”
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Comparison Theorems for the Profile Curve Equation of Rotationally Symmetric Self-Shrinkers
Topics Rotational symmetry & warped products, Stability & uniqueness · Shared terms “rotationally symmetric”
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Existence proofs for rotationally symmetric translating solutions to mean curvature flow
Topics Rotational symmetry & warped products · Shared terms “rotationally symmetric”
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Translators of the Mean Curvature Flow in Hyperbolic Einstein's Static Universe
Topics Rotational symmetry & warped products, Stability & uniqueness · Shared terms “rotationally”
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On the existence and classification of -Yamabe gradient solitons
Topics Rotational symmetry & warped products · Same author Mariel Saez · Shared terms “rotationally symmetric”
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Instability of mean curvature flow in expander coordinates
Topics Rotational symmetry & warped products · Shared terms “rotationally symmetric”, “graphical”
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Dynamical Stability of Translating Solitons to Mean Curvature Flow in Hyperbolic Space
Topics Rotational symmetry & warped products, Stability & uniqueness · Shared terms “rotationally”, “graphical”
Read around it
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In the guidebook
- 6A.10Curve Shortening and the First Geometric Flows
Shrinking circles, grim reapers, neckpinches and Huisken’s monotonicity, seen in the plane.