16 citations · 18 across the 14 of their papers we have counts for
15 papers
Free boundary and capillary minimal surfaces in spherical caps I: Low genus
Keaton Naff, Jonathan J. Zhu
This is the first of two articles in which we investigate the geometry of free boundary and capillary minimal surfaces in balls . In this article, we extend…
Linear stability and instability of Kähler Ricci solitons
Keaton Naff, Tristan Ozuch
We show that the recently discovered BCCD shrinking soliton is linearly unstable, by extending the approach of \cite{chi04} and \cite{hm11}, via recent work the \cite{cm21} on grad…
Linear stability of the blowdown Ricci shrinker in 4D
Keaton Naff, Tristan Ozuch
We prove that the four-dimensional blowdown shrinking Ricci soliton constructed by Feldman-Ilmanen-Knopf is strictly linearly stable in the sense of Cao-Hamilton-Ilmanen. This prov…
Planarity and convexity for pinched ancient solutions of mean curvature flow
Tang-Kai Lee, Keaton Naff, Jingze Zhu
We prove a parabolically scale-invariant variation of the planarity estimate in \cite{Na22} for higher codimension mean curvature flow, borrowing ideas from work of Brendle--Huiske…
Half-space intersection properties for minimal hypersurfaces
Keaton Naff, Jonathan J. Zhu
We prove ``half-space" intersection properties in three settings: the hemisphere, half-geodesic balls in space forms, and certain subsets of Gaussian space. For instance, any two e…
Moving monotonicity formulae for minimal submanifolds in constant curvature
Keaton Naff, Jonathan J. Zhu
We discover new monotonicity formulae for minimal submanifolds in space forms, which imply the sharp area bound for minimal submanifolds through a prescribed point in a geodesic ba…
The prescribed point area estimate for minimal submanifolds in constant curvature
Keaton Naff, Jonathan J. Zhu
We prove a sharp area estimate for minimal submanifolds that pass through a prescribed point in a geodesic ball in hyperbolic space, in any dimension and codimension. In certain ca…
Canonical metrics and ambiKähler structures on 4-manifolds with symmetry
Keaton Naff, Brian Weber
For -invariant 4-metrics, we show that the -flat metrics are very different from the other canonical metrics (Bach-flat, Einstein, extremal Kähler, etc). We show every $…
A local noncollapsing estimate for mean curvature flow
Simon Brendle, Keaton Naff
We prove a local version of the noncollapsing estimate for mean curvature flow. By combining our result with earlier work of X.-J. Wang, it follows that certain ancient convex solu…
Uniqueness of compact ancient solutions to the higher dimensional Ricci flow
Simon Brendle, Panagiota Daskalopoulos, Keaton Naff +1
In this paper, we study the classification of -noncollapsed ancient solutions to n-dimensional Ricci flow on , extending the result in [13] to higher dimensions. We prove t…
Rotational symmetry of ancient solutions to the Ricci flow in higher dimensions
Simon Brendle, Keaton Naff
We extend the second part of \cite{Bre20} on the uniqueness of ancient -solutions to higher dimensions. In dimensions , an ancient -solution is a nonflat, complete,…
A canonical neighborhood theorem for the mean curvature flow in higher codimension
Keaton Naff
In dimensions , we prove a canonical neighborhood theorem for the mean curvature flow of compact -dimensional submanifolds in satisfying a pinching cond…
Singularity models of pinched solutions of mean curvature flow in higher codimension
Keaton Naff
We consider ancient solutions to the mean curvature flow in () that are weakly convex, uniformly two-convex, and satisfy derivative estimates $|\nabla…
A planarity estimate for pinched solutions of mean curvature flow
Keaton Naff
We show that the blow-ups of compact solutions to the mean curvature flow in initially satisfying the pinching condition for a suitable constant $c…
Shrinking Ricci solitons with positive isotropic curvature
Keaton Naff
We show that in dimensions , a non-flat complete gradient shrinking solitons with uniformly positive isotropic curvature (PIC) must be a quotient of either the round sph…