Zobrazeno 1 - 10
of 106
pro vyhledávání: '"Sabourau, Stéphane"'
We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has a subquadratic decay at infinity, then it decomposes as a (possibly infinite) connected sum of spherical manifolds and $\math
Externí odkaz:
http://arxiv.org/abs/2407.07198
Autor:
Katz, Mikhail G., Sabourau, Stephane
More than thirty years ago, Brooks and Buser-Sarnak constructed sequences of closed hyperbolic surfaces with logarithmic systolic growth in the genus. Recently, Liu and Petri showed that such logarithmic systolic lower bound holds for every genus (no
Externí odkaz:
http://arxiv.org/abs/2407.02041
Autor:
Katz, Mikhail G., Sabourau, Stephane
We show that every closed nonpositively curved surface satisfies Loewner's systolic inequality. The proof relies on a combination of the Gauss-Bonnet formula with an averaging argument using the invariance of the Liouville measure under the geodesic
Externí odkaz:
http://arxiv.org/abs/2404.00757
Autor:
Balacheff, Florent, Sabourau, Stéphane
Publikováno v:
Annales scientifiques de l'\'Ecole Normale Sup\'erieure, S\'erie 4, Tome 43 (2010) no. 4, pp. 579-605
We prove a universal inequality between the diastole, defined using a minimax process on the one-cycle space, and the area of closed Riemannian surfaces. Roughly speaking, we show that any closed Riemannian surface can be swept out by a family of mul
Externí odkaz:
http://arxiv.org/abs/2402.01554
Autor:
Katz, Mikhail G., Sabourau, Stephane
We prove a pair of sharp reverse isoperimetric inequalities for domains in nonpositively curved surfaces: (1) metric disks centered at the vertex of a Euclidean cone of angle at least $2\pi$ have minimal area among all nonpositively curved disks of t
Externí odkaz:
http://arxiv.org/abs/2103.04661
Autor:
Katz, Mikhail G., Sabourau, Stephane
We prove an inequality of Bonnesen type for the real projective plane, generalizing Pu's systolic inequality for positively-curved metrics. The remainder term in the inequality, analogous to that in Bonnesen's inequality, is a function of R-r (suitab
Externí odkaz:
http://arxiv.org/abs/2103.02865
Autor:
Babenko, Ivan, Sabourau, Stéphane
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold $M$, and more generally of a finite simplicial complex $X$, vanishes or is positive. These topological conditions are expressed in terms of th
Externí odkaz:
http://arxiv.org/abs/2102.04551
Autor:
Cossarini, Marcos, Sabourau, Stéphane
We show that the Holmes--Thompson area of every Finsler disk of radius $r$ whose interior geodesics are length-minimizing is at least $\frac{6}{\pi} r^2$. Furthermore, we construct examples showing that the inequality is sharp and observe that the eq
Externí odkaz:
http://arxiv.org/abs/2010.00701
Autor:
Jabbour, Antonia, Sabourau, Stéphane
We establish sharp universal upper bounds on the length of the shortest closed geodesic on a punctured sphere with three or four ends endowed with a complete Riemannian metric of finite area. These sharp curvature-free upper bounds are expressed in t
Externí odkaz:
http://arxiv.org/abs/2009.10144
We show that for every closed Riemannian manifold there exists a continuous family of $1$-cycles (defined as finite collections of disjoint closed curves) parametrized by a sphere and sweeping out the whole manifold so that the lengths of all connect
Externí odkaz:
http://arxiv.org/abs/2007.14954