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 …

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 introduce a reflected chord-arc profile for curves with orthogonal boundary condition and
obtain a chord-arc estimate for embedded free boundary curve shortening flows in a convex …

We address the classification of ancient solutions to fully nonlinear curvature flows for
hypersurfaces. Under natural conditions on the speed of motion, we show that every convex …

Analogous to the bowl soliton of mean curvature flow, we construct rotationally symmetric
translating solutions to a very large class of extrinsic curvature flows, namely those whose …

We show that every convex ancient solution of mean curvature flow with Type I curvature
growth is either spherical, cylindrical, or planar. We then prove the corresponding statement …

In this paper, inspired by the work of Spruck–Xiao (Am J Math 142 (3): 993–1015, 2020) and
based partly on a result of Derdziński (Math Z 172 (3): 273–280, 1980), we prove the …

We address the classification of ancient solutions to the Gauss curvature flow under the
assumption that the solutions are contained in a cylinder of bounded cross section. For each …

Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There
has been significant progress towards the classification of such solutions under natural …

We provide several characterizations of collapsing and noncollapsing in convex ancient
mean curvature flow, establishing in particular that collapsing occurs if and only if the flow is …