We answer a long-standing open question asked by Thurston (The Geometry and Topology of Three-Manifolds. Princeton University Press, Princeton, 1978) concerning the best pinching constant for conformal metrics on S2 with one and two conical singularities of angles 2π(1+α 1) and 2π(1+α 1),2π(1+α 2) in case α 1∈(−1,0) and −1<α 1<α 2<0, respectively. The case of one conical singularity is a corollary of a result in Chen and Lin (Commun. Anal. Geom. 6(1):1–19, 1998) concerning the curvature of conformal metrics on ℝ2 with bounded Gaussian curvature 0<a≤K≤b<+∞. The case with two conical singularities is worked out by a generalization of that result.

Bartolucci, D. (2013). On the best pinching constant of conformal metrics on S^2 with one and two conical singularities. THE JOURNAL OF GEOMETRIC ANALYSIS, 23(2), 855-877 [10.1007/s12220-011-9266-0].

On the best pinching constant of conformal metrics on S^2 with one and two conical singularities

BARTOLUCCI, DANIELE
2013-01-01

Abstract

We answer a long-standing open question asked by Thurston (The Geometry and Topology of Three-Manifolds. Princeton University Press, Princeton, 1978) concerning the best pinching constant for conformal metrics on S2 with one and two conical singularities of angles 2π(1+α 1) and 2π(1+α 1),2π(1+α 2) in case α 1∈(−1,0) and −1<α 1<α 2<0, respectively. The case of one conical singularity is a corollary of a result in Chen and Lin (Commun. Anal. Geom. 6(1):1–19, 1998) concerning the curvature of conformal metrics on ℝ2 with bounded Gaussian curvature 0
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Conformal metrics – Conical singularities – Best pinching constants – Liouville type equations
project FIRB-Ideas Analysis and Beyond; MiUR project Variational methods and nonlinear PDEs
Bartolucci, D. (2013). On the best pinching constant of conformal metrics on S^2 with one and two conical singularities. THE JOURNAL OF GEOMETRIC ANALYSIS, 23(2), 855-877 [10.1007/s12220-011-9266-0].
Bartolucci, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/13671
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