On Heinz-type inequality for the half-plane and Gaussian curvature of minimal surfaces
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- by David Kalaj PDF
- Proc. Amer. Math. Soc. 148 (2020), 1757-1764 Request permission
Abstract:
We prove a Heinz-type inequality for harmonic diffeomorphisms of the half-plane onto itself. We then apply this result to prove certain sharp bound of the Gaussian curvature of a minimal surface, provided that it lies above the whole half-plane in $\mathbf {R}^3$.References
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Additional Information
- David Kalaj
- Affiliation: Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put b.b. 81000 Podgorica, Montenegro
- MR Author ID: 689421
- Email: davidk@ucg.ac.me
- Received by editor(s): January 2, 2019
- Received by editor(s) in revised form: April 13, 2019, May 18, 2019, August 22, 2019, and August 28, 2019
- Published electronically: December 30, 2019
- Communicated by: Jeremy Tyson
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1757-1764
- MSC (2010): Primary 53A10
- DOI: https://doi.org/10.1090/proc/14852
- MathSciNet review: 4069212