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A short note on rigidity of compact surfaces in space forms

Costa-Filho Wagner Oliveira

Bulletin of the Polish Academy of Sciences. Mathematics

2022

Vol. 70, no. 2

159--164

A rigidity result for a compact (without boundary) surface in a space form is obtained under a certain condition involving the Gaussian curvature and mean curvature of the surface. Moreover, as a byproduct of our approach, we shall present an alternative proof of an extension of Li’s theorem (2001) due to Chang (2013), on an integral inequality for Willmore surfaces in space forms.

Gaussian curvature of the Bergman metric with weighted Bergman kernel on the unit disc

Szajewska M.

Demonstratio Mathematica

2012

Vol. 45, nr 3

637-644

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.