Daniel Ketover

collaborators

3 papers

math.DG2025

On the existence of minimal Heegaard surfaces

Daniel Ketover, Yevgeny Liokumovich, Antoine Song

Let $H$ be a strongly irreducible Heegaard surface in a closed oriented Riemannian $3$ -manifold. We prove that $H$ is either isotopic to a minimal surface of index at most one or i…

math.DG2025

The Smale conjecture and min-max theory

Daniel Ketover, Yevgeny Liokumovich

We give a new proof of the Smale conjecture for $RP^{3}$ and all lens spaces using minimal surfaces and min-max theory. For $RP^{3}$ , the conjecture was first proved…

math.DG2024

Self-shrinkers whose asymptotic cones fatten

Daniel Ketover

For each positive integer $g$ we use variational methods to construct a genus $g$ self-shrinker $I^£_{g}$ in $R^{3}$ with entropy less than $2$ and prismatic symmetry group $\m…