arXiv subjects

Hyunsuk Kang

Publications and source records attributed to Hyunsuk Kang.

4 recordsLinked to original sources

arXiv2019

Anisotropic flow of convex hypersurfaces by the square root of the scalar curvature

We show the existence of a smooth solution for the flow deformed by the square root of the scalar curvature multiplied by a positive anisotropic factor $ψ$ given a strictly convex initial hypersurface in Euclidean space suitably pinched. We also prove the convergence of rescaled surfaces to a smooth limit manifold which is a round sphere. In dimension two, it is shown that, with a volume preserving rescaling, the limit profile satisfies a soliton equation.

math.DG↗

arXiv2013

Distribution of integral lattice points in an ellipsoid with a diophantine center

We evaluate the mean square limit of exponential sums related with a rational ellipsoid, extending a work of Marklof. Moreover, as a result of it, we study the asymptotic values of the normalized deviations of the number of lattice points inside a rational ellipsoid and inside a rational thin ellipsoidal shell.

math.NT↗

arXiv2010

Comparison of Invariant Metrics

We estimate the boundary behavior of the Kobayashi metric on $\C\sm\set{0,1}$. We also compare the Bergman metric on the ring domain in $\C^{2}$ to the Bergman metric on the ball.

math.CV↗

arXiv2005

Isospectral surfaces of genus 2 and 3

We give examples of isospectral non-isometric surfaces of genus 2 and 3 with variable curvatures and apply the result to construct isospectral potentials on Riemann surfaces of genus 2.

math.DG↗