Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 203-215 (1999)

Curve Shortening Flow and the Banchoff-Pohl Inequality on Surfaces of Nonpositive Curvature

Bernd Süssmann

Universität Stuttgart, Mathematisches Institut B, Pfaffenwaldring 57, 70569 Stuttgart, Germany

Abstract: In this paper the classical Banchoff-Pohl inequality, an isoperimetric inequality for nonsimple closed curves in the Euclidean plane, involving the square of the winding number, is generalized to nonpositively curved surfaces. The proof uses the well-known curve shortening flow.

Classification (MSC91): 53C40; 53A04, 53C65

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