We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian
manifolds, including mean curvature flow and harmonic map heat flow. Our work has various …

We survey some ideas regarding the application of the Aleksandrov reflection method in
partial differential equation to extrinsic geometric flows of Euclidean hypersurfaces. In this …

We construct a compact, convex ancient solution of mean curvature flow in $\mathbb {R}^{n+
1} $ with $ O (1)\times O (n) $ symmetry that lies in a slab of width $\pi $. We provide detailed …

Convex ancient solutions to curve shortening flow | SpringerLink Skip to main content
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Ancient mean curvature flows out of polytopes Page 1 GGG G G G G GGGG G G G GGG
TTT T T T TTTTTT T T T T T Geometry & Topology msp Volume 26 (2022) Ancient mean …

We construct a compact, convex ancient solution of mean curvature flow in $\mathbb R^{n+
1} $ with $ O (1)\times O (n) $ symmetry that lies in a slab of width $\pi $. We provide detailed …

We prove several sharp one-sided pinching estimates for immersed and embedded
hypersurfaces evolving by various fully nonlinear, one-homogeneous curvature flows by the …

We prove rigidity theorems for ancient solutions of geometric flows of immersed
submanifolds. Specifically, we find pinching conditions on the second fundamental form that …

On the Discrete Spectrum of Robin Laplacians in Conical Domains Page 1 “cone18-mmnp” —
2016/2/26 — 21:23 — page 100 — #1 ✐ ✐ ✐ ✐ Math. Model. Nat. Phenom. Vol. 11, No. 2, 2016 …

We consider the evolution of hypersurfaces on the unit sphere $\mathbb {S}^{n+ 1} $ by
smooth functions of the Weingarten map. We introduce the notion ofquasi-ancient'solutions …