On isoperimetric and Fejér-Riesz inequality for harmonic surfaces

Details On isoperimetric and Fejér-Riesz inequality for harmonic surfaces On isoperimetric and Fejér-Riesz inequality for harmonic surfaces

2011-05-02

arxiv.org/abs/1105.0273v2

Mathematics

Complex Variables

12 pages

Scientific paper

In this paper we discus Fej\'er-Riesz inequality and isoperimetric inequality for holomorphic surfaces, harmonic surfaces and Riemann surfaces. Among the other results we prove an isoperimetric inequality for disk-type harmonic surfaces in Euclidean space $\mathbf R^n$ with rectifiable boundary and show that the geodesic diameter of a simply connected harmonic surface embedded in the Euclidean space $\mathbf R^n$ is smaller than one half of its Euclidean perimeter.

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