We study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface Σ admitting conical singularities of orders αi ’s at points pi ’s. In particular, we are concerned with the case where the prescribed Gaussian curvature is sign-changing. Such a geometrical problem reduces to solving a singular Liouville equation. By employing a min–max scheme jointly with a finite dimensional reduction method, we deduce new perturbative results providing existence when the quantity χ(Σ)+∑iαi approaches a positive even integer, where χ(Σ) is the Euler characteristic of the surface Σ .

D'Aprile, T., De Marchis, F., Ianni, I. (2018). Prescribed Gauss curvature problem on singular surfaces. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 57(4) [10.1007/s00526-018-1373-3].

Prescribed Gauss curvature problem on singular surfaces

D'Aprile T.;
2018-08-01

Abstract

We study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface Σ admitting conical singularities of orders αi ’s at points pi ’s. In particular, we are concerned with the case where the prescribed Gaussian curvature is sign-changing. Such a geometrical problem reduces to solving a singular Liouville equation. By employing a min–max scheme jointly with a finite dimensional reduction method, we deduce new perturbative results providing existence when the quantity χ(Σ)+∑iαi approaches a positive even integer, where χ(Σ) is the Euler characteristic of the surface Σ .
ago-2018
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
D'Aprile, T., De Marchis, F., Ianni, I. (2018). Prescribed Gauss curvature problem on singular surfaces. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 57(4) [10.1007/s00526-018-1373-3].
D'Aprile, T; De Marchis, F; Ianni, I
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/199392
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