arXiv subjects

Hwajeong Kim

Publications and source records attributed to Hwajeong Kim.

4 recordsLinked to original sources

arXiv2013

A note on generalized Dirac eigenvalues for split holonomy and torsion

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\inΛ^3 M$ in the situation where the tangent bundle splits under the holonomy of $\nabla$ and the torsion of $\nabla$ is of `split' type. We prove an optimal lower bound for the first eigenvalue of the Dirac operator with torsion that generalizes Friedrich's classical Riemannian estimate.

math.DG↗

arXiv2013

Twistorial eigenvalue estimates for generalized Dirac operators with torsion

We study the Dirac spectrum on compact Riemannian spin manifolds $M$ equipped with a metric connection $\nabla$ with skew torsion $T\inΛ^3M$ by means of twistor theory. An optimal lower bound for the first eigenvalue of the Dirac operator with torsion is found that generalizes Friedrich's classical Riemannian estimate. We also determine a novel twistor and Killing equation with torsion and use it to discuss the case in which the minimum is attained in the bound.

math.DG↗

arXiv2008

Unstable minimal surfaces of annulus type in manifolds

Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We extend this theory for obtaining unstable minimal surfaces in Riemannian manifolds. In particular, we handle minimal surfaces of annulus type, i.e. we prescribe two Jordan curves of class $C^3$ in a Riemannian manifold and prove the existence of unstable minimal surfaces of annulus type bounded by these curves.

math.DG↗

arXiv2006

A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifolds

Given two Jordan curves in a Riemannian manifold, a minimal surface of annulus type bounded by these curves is described as the harmonic extension of a critical point of some functional (the Dirichlet integral) in a certain space of boundary parametrizations. The $H^{2,2}$-regularity of the minimal surface of annulus type will be proved by applying the critical points theory and Morrey's growth condition.

math.DG↗