Total Curvature and the Isoperimetric Inequality in Cartan–Hadamard Manifolds

We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.

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Veröffentlicht in:	The Journal of Geometric Analysis 2022-02, Vol.32 (2), Article 50
Hauptverfasser:	Ghomi, Mohammad, Spruck, Joel
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Curvature Differential Geometry Dynamical Systems and Ergodic Theory Equality Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Isoperimetric problem Mathematics Mathematics and Statistics Riemann manifold
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Beschreibung
Zusammenfassung:	We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-021-00801-2