Zobrazeno 1 - 10
of 48
pro vyhledávání: '"secondary: 53c23"'
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:
Fukaya, Tomohiro
We show that a Busemann space $X$ which is covered by parallel bi-infinite geodesics is homeomorphic to a product of another Busemann space $Y$ and the real line. We also show that a semi-simple isometry on $X$ preserving the foliation by parallel ge
Externí odkaz:
http://arxiv.org/abs/2206.01924
We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the measure of unit balls is uniformly bounded
Externí odkaz:
http://arxiv.org/abs/2201.03525
Autor:
Hsiao, E., Kotschick, D.
Publikováno v:
Bull. London Math. Soc. 54 (2022), 2314--2323
We prove that any rational linear combination of Pontryagin numbers that does not factor through the universal elliptic genus is unbounded on connected closed spin manifolds of nonnegative sectional curvature.
Comment: 9 pages, final version, to
Comment: 9 pages, final version, to
Externí odkaz:
http://arxiv.org/abs/2111.07862
Autor:
Chen, Lizhi
Let $M$ be a closed $n$-manifold with nonzero simplicial volume. A central result in systolic geometry from Gromov is that systolic volume of $M$ is related to its simplicial volume. In this short note, we show that systolic volume of hyperbolic mani
Externí odkaz:
http://arxiv.org/abs/2109.09194
Autor:
Plaut, Conrad
We define the compact universal cover of a compact, metrizable connected space (i.e. a continuum) X to be the inverse limit of all continua that regularly cover X. We show that such covers do indeed form an inverse system with bonding maps that are r
Externí odkaz:
http://arxiv.org/abs/2109.02152
Publikováno v:
Analysis & PDE 17 (2024) 455-498
We represent minimal upper gradients of Newtonian functions, in the range $1\le p<\infty$, by maximal directional derivatives along "generic" curves passing through a given point, using plan-modulus duality and disintegration techniques. As an applic
Externí odkaz:
http://arxiv.org/abs/2102.08097
Publikováno v:
Anal. Geom. Metr. Spaces 10 (2022), no. 1, 344-372
We consider functions with an asymptotic mean value property, known to characterize harmonicity in Riemannian manifolds, in doubling metric measure spaces. We show that the strongly amv-harmonic functions are H\"older continuous for any exponent belo
Externí odkaz:
http://arxiv.org/abs/2005.13902
In this paper we discuss three distance functions on the set of convex bodies. In particular we study the convergence of Delzant polytopes, which are fundamental objects in symplectic toric geometry. By using these observations, we derive some conver
Externí odkaz:
http://arxiv.org/abs/2003.02293
Publikováno v:
Pacific J. Math. 315 (2021) 27-44
In this paper, we study locally strongly convex Tchebychev hypersurfaces, namely the {\it centroaffine totally umbilical hypersurfaces}, in the $(n+1)$-dimensional affine space $\mathbb{R}^{n+1}$. We first make an ordinary-looking observation that su
Externí odkaz:
http://arxiv.org/abs/1911.05222