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

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.
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: http://hdl.handle.net/11590/380327
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