Best constants for metric space inversion inequalities

• Autorzy: Stephen Buckley , Safia Hamza
• Języki publikacji: EN

Abstrakty

EN

For every metric space (X, d) and origin o ∈ X, we show the inequality I o(x, y) ≤ 2d o(x, y), where I o(x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o, and x, y ∈ X \ {o} The constant 2 is best possible.

Słowa kluczowe

EN

Metric space inversion; Best constant

Kategorie tematyczne

• 54E25: Semimetric spaces
• 30F45: Conformal metrics (hyperbolic, Poincar\'e, distance functions)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 5
• Strony: 865-875

Daty

wydano

2013-05-01

online

2013-03-14

Twórcy

autor

Stephen Buckley

• National University of Ireland Maynooth

autor

Safia Hamza

• National University of Ireland Maynooth

Bibliografia

• [1] Bonk M., Heinonen J., Koskela P., Uniformizing Gromov Hyperbolic Spaces, Astérisque, 207, Société Mathématique de France, Paris, 2001
• [2] Buckley S.M., Falk K., Wraith D.J., Ptolemaic spaces and CAT(0), Glasg. Math. J., 2009, 51(2), 301–314 http://dx.doi.org/10.1017/S0017089509004984
• [3] Buckley S.M., Herron D.A., Xie X., Metric space inversions, quasihyperbolic distance, and uniform spaces, Indiana Univ. Math. J., 2008, 57(2), 837–890
• [4] Buckley S.M., Wraith D.J., McDougall J., On Ptolemaic metric simplicial complexes, Math. Proc. Cambridge Philos. Soc., 2010, 149(1), 93–104 http://dx.doi.org/10.1017/S0305004110000125
• [5] Foertsch T., Lytchak A., Schroeder V., Nonpositive curvature and the Ptolemy inequality, Int. Math. Res. Not. IMRN, 2007, 22, #rnm100
• [6] Foertsch T., Schroeder V., Hyperbolicity, CAT(−1)-spaces and the Ptolemy inequality, Math. Ann., 2011, 350(2), 339–356 http://dx.doi.org/10.1007/s00208-010-0560-0
• [7] Herron D., Shanmugalingam N., Xie X., Uniformity from Gromov hyperbolicity, Illinois J. Math., 2008, 52(4), 1065–1109

Identyfikatory

DOI

10.2478/s11533-013-0213-0