Ancient asymptotically cylindrical flows and applications
In this paper, we prove the mean-convex neighborhood conjecture for neck singularities of
the mean curvature flow in R n+ 1 for all n≥ 3: we show that if a mean curvature flow {M t} in …
the mean curvature flow in R n+ 1 for all n≥ 3: we show that if a mean curvature flow {M t} in …
Mean curvature flow with generic initial data
We show that the mean curvature flow of generic closed surfaces in\(\mathbb {R}^{3}\)
avoids asymptotically conical and non-spherical compact singularities. We also show that …
avoids asymptotically conical and non-spherical compact singularities. We also show that …
Mean convex smoothing of mean convex cones
Z Wang - Geometric and Functional Analysis, 2024 - Springer
We show that any minimizing hypercone can be perturbed into one side to a properly
embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity …
embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity …
A mountain-pass theorem for asymptotically conical self-expanders
J Bernstein, L Wang - Peking Mathematical Journal, 2022 - Springer
We develop a min–max theory for asymptotically conical self-expanders of mean curvature
flow. In particular, we show that given two distinct strictly stable self-expanders that are …
flow. In particular, we show that given two distinct strictly stable self-expanders that are …
Mean curvature flow with generic low-entropy initial data
O Chodosh, K Choi, C Mantoulidis… - Duke Mathematical …, 2024 - projecteuclid.org
We prove that sufficiently low-entropy closed hypersurfaces can be perturbed so that their
mean curvature flow encounters only spherical and cylindrical singularities. Our theorem …
mean curvature flow encounters only spherical and cylindrical singularities. Our theorem …
Relative expander entropy in the presence of a two-sided obstacle and applications
J Bernstein, L Wang - Advances in Mathematics, 2022 - Elsevier
We study a notion of relative entropy motivated by self-expanders of mean curvature flow. In
particular, we obtain the existence of this quantity for arbitrary hypersurfaces trapped …
particular, we obtain the existence of this quantity for arbitrary hypersurfaces trapped …
Existence of monotone morse flow lines of the expander functional
J Bernstein, L Chen, L Wang - arXiv preprint arXiv:2404.08541, 2024 - arxiv.org
arXiv:2404.08541v1 [math.DG] 12 Apr 2024 Page 1 arXiv:2404.08541v1 [math.DG] 12 Apr
2024 EXISTENCE OF MONOTONE MORSE FLOW LINES OF THE EXPANDER FUNCTIONAL …
2024 EXISTENCE OF MONOTONE MORSE FLOW LINES OF THE EXPANDER FUNCTIONAL …
Rotational symmetry of solutions of mean curvature flow coming out of a double cone II
L Chen - Calculus of Variations and Partial Differential …, 2023 - Springer
Given a double cone C with entropy at most two that is symmetric across some hyperplane,
we show that any integral Brakke flow coming out of the cone must inherit the reflection …
we show that any integral Brakke flow coming out of the cone must inherit the reflection …
On the existence and uniqueness of ancient rescaled mean curvature flows
L Chen - arXiv preprint arXiv:2212.10798, 2022 - arxiv.org
We show existence of ancient solutions to the rescaled mean curvature flow starting from a
given asymptotically conical self-expander. These are examples of mean curvature flows …
given asymptotically conical self-expander. These are examples of mean curvature flows …
Closed hypersurfaces of low entropy in are isotopically trivial
J Bernstein, L Wang - Duke Mathematical Journal, 2022 - projecteuclid.org
Closed hypersurfaces of low entropy in R4 are isotopically trivial Page 1 CLOSED
HYPERSURFACES OF LOW ENTROPY IN R4 ARE ISOTOPICALLY TRIVIAL JACOB …
HYPERSURFACES OF LOW ENTROPY IN R4 ARE ISOTOPICALLY TRIVIAL JACOB …