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pro vyhledávání: '"Ketover, Daniel"'
We use variational methods to construct a free boundary minimal surface in the three-dimensional unit ball with genus one, two boundary components and prismatic symmetry. Key ingredients are an extension of the equivariant min-max theory to include o
Externí odkaz:
http://arxiv.org/abs/2409.12588
Autor:
Ketover, Daniel
For each positive integer $g$ we use variational methods to construct a genus $g$ self-shrinker $\Sigma_g$ in $\mathbb{R}^3$ with entropy less than $2$ and prismatic symmetry group $\mathbb{D}_{g+1}\times\mathbb{Z}_2$. For $g$ sufficiently large, the
Externí odkaz:
http://arxiv.org/abs/2407.01240
Autor:
Ketover, Daniel, Liokumovich, Yevgeny
We give a new proof of the Smale conjecture for $\mathbb{RP}^3$ and all lens spaces using minimal surfaces and min-max theory. For $\mathbb{RP}^3$, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.
Comment: Updated vers
Comment: Updated vers
Externí odkaz:
http://arxiv.org/abs/2310.05756
Autor:
Haslhofer, Robert, Ketover, Daniel
In this paper, we prove that every strictly convex 3-ball with nonnegative Ricci-curvature contains at least 3 embedded free-boundary minimal 2-disks for any generic metric, and at least 2 solutions even without genericity assumption. Our approach co
Externí odkaz:
http://arxiv.org/abs/2307.01828
Autor:
Ketover, Daniel
We show that the number of genus $g$ embedded minimal surfaces in $\mathbb{S}^3$ tends to infinity as $g\rightarrow\infty$. The surfaces we construct resemble doublings of the Clifford torus with curvature blowing up along torus knots as $g\rightarro
Externí odkaz:
http://arxiv.org/abs/2211.03745
We survey some recent geometric methods for studying Heegaard splittings of 3-manifolds
Externí odkaz:
http://arxiv.org/abs/2002.00445
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 isotopic to the boundary of a tubular neighborhood about a non-orientab
Externí odkaz:
http://arxiv.org/abs/1911.07161
Autor:
Ketover, Daniel, Liokumovich, Yevgeny
We show that on any Riemannian surface for each $0
Externí odkaz:
http://arxiv.org/abs/1810.09308
Autor:
Chodosh, Otis, Ketover, Daniel
Let $(M,g)$ be an asymptotically flat $3$-manifold containing no closed embedded minimal surfaces. We prove that for every point $p\in M$ there exists a complete properly embedded minimal plane in $M$ containing $p$.
Comment: final version, to a
Comment: final version, to a
Externí odkaz:
http://arxiv.org/abs/1709.09650
Autor:
Ketover, Daniel, Liokumovich, Yevgeny
We prove that for generic metrics on a 3-sphere, the minimal surface obtained from the min-max procedure of Simon-Smith has index 1. We prove an analogous result for minimal surfaces arising from strongly irreducible Heegaard sweepouts in 3-manifolds
Externí odkaz:
http://arxiv.org/abs/1709.09744