Results 11 to 20 of about 658 (33)
The homology systole of hyperbolic Riemann surfaces [PDF]
, 2011 The main goal of this note is to show that the study of closed hyperbolic surfaces with maximum length systole is in fact the study of surfaces with maximum length homological systole.
Parlier, Hugo
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On the existence of orthonormal geodesic bases for Lie algebras [PDF]
, 2013 We show that every unimodular Lie algebra, of dimension at most 4, equipped with an inner product, possesses an orthonormal basis comprised of geodesic elements.
Cairns, Grant +3 more
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Global Gronwall Estimates for Integral Curves on Riemannian Manifolds [PDF]
, 2006 We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors.
Kunzinger, Michael +3 more
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The Length of a Shortest Geodesic Loop [PDF]
, 2007 We give a lower bound for the length of a non-trivial geodesic loop on a simply-connected and compact manifold of even dimension with a non-reversible Finsler metric of positive flag curvature. Harris and Paternain use this estimate in their recent paper
Rademacher, Hans-Bert
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A Zoll counterexample to a geodesic length conjecture [PDF]
, 2007 We construct a counterexample to a conjectured inequality ...
Balacheff, Florent +2 more
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Geodesic excursions into cusps in finite-volume hyperbolic manifolds [PDF]
, 1993 18 pages, no figures.-- MSC1991 codes: Primary: 53C22; Secondary: 30F40, 58F17.MR#: MR1214056 (94d:53067)Zbl#: Zbl 0793.53052The main goal of the paper is to prove that, for a given non-compact hyperbolic $n$-manifold $M$ of finite volume, $p\in M$, and ...
Melián, M. Victoria, Pestana, Domingo
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Lagrangian non-squeezing and a geometric inequality
, 2013 We prove that if the unit codisc bundle of a closed Riemannian manifold embeds symplectically into a symplectic cylinder of radius one then the length of the shortest nontrivial closed geodesic is at most half the area of the unit disc.Comment: minor ...
Zehmisch, Kai
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On geodesic envelopes and caustics [PDF]
, 2005 We give a global description of envelopes of geodesic tangents of regular curves in (not necessarily convex) Riemannian surfaces. We prove that such an envelope is the union of the curve itself, its inflectional geodesics and its tangential caustics ...
Capitanio, Gianmarco
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Non-existence of certain type of convex functions on a Riemannian manifold with a pole
, 2018 This paper is devoted to the study of non-existence of certain type of convex functions on a Riemannian manifold with a pole. To this end, we have developed the notion of odd and even function on a Riemannian manifold with a pole and proved the non ...
Ahmad, Izhar +2 more
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Rigidity and flexibility of surface groups [PDF]
, 2004 The aim of this work is the °exibility of the hyperbolic surfaces. The results are about °exibility and geometrical boundedness. Bers are stated the universal property for all hyperbolic surface of ¯nite area where introduced the constant of boundedness.
Grácio, Clara, Ramos, José Sousa
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