Sub-Finsler Horofunction Boundaries of the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2021 We give a complete analytic and geometric description of the horofunction boundary for polygonal sub-Finsler metrics, that is, those that arise as asymptotic cones of word metrics, on the Heisenberg group.
Fisher Nate, Golo Sebastiano Nicolussi
doaj +1 more source
A systolic inequality with remainder in the real projective plane
Open Mathematics, 2020 The first paper in systolic geometry was published by Loewner’s student P. M. Pu over half a century ago. Pu proved an inequality relating the systole and the area of an arbitrary metric in the real projective plane.
Katz Mikhail G., Nowik Tahl
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Connected components of the compactification of representation spaces of surface groups [PDF]
, 2008 The Thurston compactification of Teichmuller spaces has been generalised to many different representation spaces by Morgan, Shalen, Bestvina, Paulin, Parreau and others.
M. Wolff
semanticscholar +1 more source
Lipschitz minimality of the multiplication maps of unit complex, quaternion and octonion numbers [PDF]
, 2013 We prove that the multiplication maps S n S n ! S n (nD 1;3;7) for unit complex, quaternion and octonion numbers are, up to isometries of domain and range, the unique Lipschitz constant minimizers in their homotopy classes.
Haomin Wen
semanticscholar +1 more source
On the problem of prescribing weighted scalar curvature and the weighted Yamabe flow
Analysis and Geometry in Metric Spaces, 2023 The weighted Yamabe problem introduced by Case is the generalization of the Gagliardo-Nirenberg inequalities to smooth metric measure spaces. More precisely, given a smooth metric measure space (M,g,e−ϕdVg,m)\left(M,g,{e}^{-\phi }{\rm{d}}{V}_{g},m), the ...
Ho Pak Tung, Shin Jinwoo
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Parabolic isometries of CAT(0) spaces and CAT(0) dimensions (Perspectives of Hyperbolic Spaces II) [PDF]
, 2003 We study discrete groups from the view point of a dimension gap in connection to CAT(0) geometry. Developing studies by Brady-Crisp and Bridson, we show that there exist nitely presented groups of geometric dimension 2 which do not act properly on any ...
K. Fujiwara, T. Shioya, S. Yamagata
semanticscholar +1 more source
Branching Geodesics of the Gromov-Hausdorff Distance
Analysis and Geometry in Metric Spaces, 2022 In this paper, we first evaluate topological distributions of the sets of all doubling spaces, all uniformly disconnected spaces, and all uniformly perfect spaces in the space of all isometry classes of compact metric spaces equipped with the Gromov ...
Ishiki Yoshito
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On the topology of closed manifolds with quasi-constant sectional curvature
Journal de l'École polytechnique. Mathématiques, 2019 We prove that closed manifolds admitting a metric whose sectional curvature is locally quasi-constant are graphs of space forms. In the more general setting of QC space where sets of isotropic points are arbitrary, under suitable positivity assumption ...
L. Funar
semanticscholar +1 more source
A Zoll counterexample to a geodesic length conjecture [PDF]
, 2007 We construct a counterexample to a conjectured inequality ...
Balacheff, Florent +2 more
core +6 more sources
On the structure of Riemannian manifolds of almost nonnegative Ricci curvature
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 39, Page 2085-2090, 2004., 2004 We study the structure of manifolds with almost nonnegative Ricci curvature. We prove a compact Riemannian manifold with bounded curvature, diameter bounded from above, and Ricci curvature bounded from below by an almost nonnegative real number such that the first Betti number havingcodimension two is an infranilmanifold or a finite cover is a sphere ...
Gabjin Yun
wiley +1 more source