Gaussian curvature of minimal graphs in M×R

Gaussian curvature of minimal graphs in M×R

In this paper, we consider minimal graphs in the three-dimensional Riemannian manifold M×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 represent...

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Veröffentlicht in:Journal of mathematical analysis and applications 2024-01, Vol.529 (1), p.127589, Article 127589
1. Verfasser: Kalaj, David
Format: Artikel
Sprache:eng
Schlagworte:
Harmonic mappings
Minimal surfaces
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Zusammenfassung:In this paper, we consider minimal graphs in the three-dimensional Riemannian manifold M×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 ℘-harmonic mappings. We also prove some Schwarz lemma type results and some Heinz type results for harmonic mappings between geodesic disks in Riemannian surfaces.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127589