Complexity of parabolic systems
TH Colding, WP Minicozzi - Publications mathématiques de l'IHÉS, 2020 - Springer
We first bound the codimension of an ancient mean curvature flow by the entropy. As a
consequence, all blowups lie in a Euclidean subspace whose dimension is bounded by the …
consequence, all blowups lie in a Euclidean subspace whose dimension is bounded by the …
Eigenvalues of the drifted Laplacian on complete metric measure spaces
In this paper, first we study a complete smooth metric measure space (M n, g, e− fdv) with the
(∞)-Bakry–Émery Ricci curvature Ric f≥ a 2 g for some positive constant a. It is known that …
(∞)-Bakry–Émery Ricci curvature Ric f≥ a 2 g for some positive constant a. It is known that …
[HTML][HTML] Topics in differential geometry associated with position vector fields on Euclidean submanifolds
BY Chen - Arab Journal of Mathematical Sciences, 2017 - Elsevier
The position vector field is the most elementary and natural geometric object on a Euclidean
submanifold. The purpose of this article is to survey six research topics in differential …
submanifold. The purpose of this article is to survey six research topics in differential …
Uniqueness of conical singularities for mean curvature flows
TK Lee, X Zhao - Journal of Functional Analysis, 2024 - Elsevier
Uniqueness of conical singularities for mean curvature flows - ScienceDirect Skip to main
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Mean curvature flow by the Allen–Cahn equation
DS Lee, JS Kim - European Journal of Applied Mathematics, 2015 - cambridge.org
In this paper, we investigate motion by mean curvature using the Allen–Cahn (AC) equation
in two and three space dimensions. We use an unconditionally stable hybrid numerical …
in two and three space dimensions. We use an unconditionally stable hybrid numerical …
Regularity of elliptic and parabolic systems
TH Colding, WP Minicozzi II - arXiv preprint arXiv:1905.00085, 2019 - arxiv.org
We show uniqueness of cylindrical blowups for mean curvature flow in all dimension and all
codimension. Cylindrical singularities are known to be the most important; they are the most …
codimension. Cylindrical singularities are known to be the most important; they are the most …
Remarks on the self-shrinking Clifford torus
On the one hand, we prove that the Clifford torus in ℂ 2 is unstable for Lagrangian mean
curvature flow under arbitrarily small Hamiltonian perturbations, even though it is …
curvature flow under arbitrarily small Hamiltonian perturbations, even though it is …
A strong Frankel Theorem for shrinkers
TH Colding, WP Minicozzi II - arXiv preprint arXiv:2306.08078, 2023 - arxiv.org
We prove a strong Frankel theorem for mean curvature flow shrinkers in all dimensions: Any
two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must …
two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must …
Skew mean curvature flow
C Song, J Sun - Communications in Contemporary Mathematics, 2019 - World Scientific
The skew mean curvature flow (SMCF), which origins from the study of fluid dynamics,
describes the evolution of a codimension two submanifold along its binormal direction. We …
describes the evolution of a codimension two submanifold along its binormal direction. We …
[PDF][PDF] In search of stable geometric structures
TH Colding, WP Minicozzi II - arXiv preprint arXiv:1907.03672, 2019 - arxiv.org
arXiv:1907.03672v1 [math.DG] 8 Jul 2019 Page 1 IN SEARCH OF STABLE GEOMETRIC
STRUCTURES TOBIAS HOLCK COLDING AND WILLIAM P. MINICOZZI II Abstract. We will …
STRUCTURES TOBIAS HOLCK COLDING AND WILLIAM P. MINICOZZI II Abstract. We will …