16 citations · 55 across the 13 of their papers we have counts for
14 papers
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…
Type II smoothing in mean curvature flow
Sigurd Angenent, Panagiota Daskalopoulos, Natasa Sesum
In 1994 Velazquez constructed a smooth \(O(4)\times O(4)\) invariant Mean Curvature Flow that forms a type-II singularity at the origin in space-time. Stolarski very recently showe…
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…
Nonstandard existence proofs for reaction diffusion equations
Connor Olson, Marshall Mueller, Sigurd B. Angenent
We give an existence proof for distribution solutions to a scalar reaction diffusion equation, with the aim of illustrating both the differences and the common ingredients of the n…