Abstract
Let M and \(\tilde M\)be complete surfaces such that the respective sectional curvatures satisfy \(K \geqslant \widetilde{\rm K}\). It is shown that the volumes of geodesic balls satisfy \(V_m (r) \leqslant \tilde V_{\tilde m} (r)\). If M and \(\tilde M\)are compact and simply connected then vol(M)≤vol(\(\tilde M\)).
Keywords
- Vector Bundle
- Sectional Curvature
- Gaussian Curvature
- Riccati Equation
- Comparison Theorem
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© 1985 Springer-Verlag
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Gray, A. (1985). Comparison theorems for volumes in surfaces. In: Geometry and Topology. Lecture Notes in Mathematics, vol 1167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075219
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DOI: https://doi.org/10.1007/BFb0075219
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16053-3
Online ISBN: 978-3-540-39738-0
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