Daniel Ketover

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20162022

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math.DG2022

Flipping Heegaard splittings and minimal surfaces

Daniel Ketover

We show that the number of genus $g$ embedded minimal surfaces in $S^{3}$ tends to infinity as $g \to \infty$ . The surfaces we construct resemble doublings of the Clif…

math.DG2018

On the existence of closed $C^{1, 1}$ curves of constant curvature

Daniel Ketover, Yevgeny Liokumovich

We show that on any Riemannian surface for each $0 < c < \infty$ there exists an immersed $C^{1, 1}$ curve that is smooth and with curvature equal to $\pm c$ away from a point. We give…

math.DG2016

Self-shrinking Platonic solids

Daniel Ketover

We construct new embedded self-shrinkers of genus 3, 5, 7, 11 and 19 using variational methods. Our self-shrinkers resemble doublings of the Platonic solids and were discovered num…

Flipping Heegaard splittings and minimal surfaces

On the existence of closed C1,1 curves of constant curvature

Self-shrinking Platonic solids

On the existence of closed $C^{1, 1}$ curves of constant curvature