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

DOI10.1007/s12220-011-9266-0zbMath1269.30045OpenAlexW2012269792MaRDI QIDQ1948734

Daniele Bartolucci

Publication date: 24 April 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-011-9266-0

zbMATH Keywords

cone singularitiespinching constantbad 2-orbifoldconformal metric on the 2-sphere

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) General geometric structures on low-dimensional manifolds (57M50)

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Cites Work

• Unnamed Item
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• Gaussian curvature on singular surfaces
• Zur isoperimetrischen Ungleichung auf gekrümmten Flächen
• A sharp sup+inf inequality for a nonlinear elliptic equation in \(\mathbb{R}^2\)
• Prescribing Gaussian curvatures on surfaces with conical singularities
• Prescribed curvature and singularities of conformal metrics on Riemann surfaces
• Qualitative properties of solutions to some nonlinear elliptic equations in \(\mathbb{R}^2\)
• Explicit construction of extremal Hermitian metrics with finite conical singularities on \(S^2\)
• What kinds of singular surfaces can admit constant curvature?
• Supercritical Conformal Metrics on Surfaces with Conical Singularities
• Prescribing Curvature on Compact Surfaces with Conical Singularities
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Liouville Equation and Spherical Convex Polytopes
• Elastic waves in rods and clad rods
• Metrics of positive curvature with conic singularities on the sphere

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