16 citations · 55 across the 13 of their papers we have counts for
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Nonconvex ancient solutions to Curve Shortening Flow
Yongzhe Zhang, Connor Olson, Ilyas Khan +1
We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For it is approximated by the rotating Yin-Yang soliton, tru…
Unique Asymptotics of Compact Ancient Solutions to three-dimensional Ricci flow
Sigurd Angenent, Simon Brendle, Panagiota Daskalopoulos +1
We consider compact ancient solutions to the three-dimensional Ricci flow which are noncollapsed. We prove that such a solutions is either a family of shrinking round spheres, or i…
Ricci Solitons, Conical Singularities, and Nonuniqueness
Sigurd B. Angenent, Dan Knopf
In dimension , there is a complete theory of weak solutions of Ricci flow - the singular Ricci flows introduced by Kleiner and Lott - which are unique across singularities, as…
Unique asymptotics of ancient compact non-collapsed solutions to the 3-dimensional Ricci flow
Sigurd Angenent, Panagiota Daskalopoulos, Natasa Sesum
We consider compact noncollapsed ancient solutions to the 3-dimensional Ricci flow that are rotationally and reflection symmetric. We prove that these solutions are either the sphe…
Uniqueness of two-convex closed ancient solutions to the mean curvature flow
Sigurd B. Angenent, Panagiota Daskalopoulos, Natasa Sesum
In this paper we consider closed non-collapsed ancient solutions to the mean curvature flow () which are uniformly two-convex. We prove that any two such ancient solutions…
Ancient Solutions to Curve Shortening with Finite Total Curvature
Sigurd Angenent, Qian You
We construct ancient solutions to Curve Shortening in the plane whose total curvature is uniformly bounded by gluing together an arbitrary chain of given Grim Reapers along their c…