We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk. This is equivalent to solving the following P.D.E. {-Δu=2K(z)euinD2,∂νu+2=2h(z)eu2on∂D2,where K, h are the prescribed curvatures. We construct a family of conformal metrics with curvatures Kε, hε converging to K, h respectively as ε goes to 0, which blows up at one boundary point under some generic assumptions.

Battaglia, L., Medina, M., Pistoia, A. (2021). Large conformal metrics with prescribed Gaussian and geodesic curvatures. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 60(1) [10.1007/s00526-020-01872-9].

Large conformal metrics with prescribed Gaussian and geodesic curvatures

Battaglia L.;
2021-01-01

Abstract

We consider the problem of prescribing Gaussian and geodesic curvatures for a conformal metric on the unit disk. This is equivalent to solving the following P.D.E. {-Δu=2K(z)euinD2,∂νu+2=2h(z)eu2on∂D2,where K, h are the prescribed curvatures. We construct a family of conformal metrics with curvatures Kε, hε converging to K, h respectively as ε goes to 0, which blows up at one boundary point under some generic assumptions.
2021
Battaglia, L., Medina, M., Pistoia, A. (2021). Large conformal metrics with prescribed Gaussian and geodesic curvatures. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 60(1) [10.1007/s00526-020-01872-9].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/380327
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