Gaussian curvature of minimal graphs in $M\times \mathbb{R}$

David Kalaj

Gaussian curvature of minimal graphs in $M\times \mathbb{R}$

Differential Geometry 2022-07-12 v1

Authors: David Kalaj

Abstract

In this paper, we consider minimal graphs in the three-dimensional Riemannian manifold $M\times\mathbb{R}$ . We mainly estimate the Gaussian curvature of such surfaces. We consider the minimal disks and minimal graphs bounded by two Jordan curves in parallel planes. The key to the proofs is the Weierstrass representation of those surfaces via $\wp-$ harmonic mappings. We also prove some Schwarz lemma type results and some Heinz type results for harmonic mappings between geodesic disks in Riemannian surfaces.

Keywords

minimal graphs gaussian curvature weierstrass representation wp-harmonic mappings schwarz lemma heinz type results riemannian manifold

Cite

@article{arxiv.2207.04769,
  title  = {Gaussian curvature of minimal graphs in $M\times \mathbb{R}$},
  author = {David Kalaj},
  journal= {arXiv preprint arXiv:2207.04769},
  year   = {2022}
}

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