This paper deals with the singular Liouville equation −Δgu=ρ(h(x)e2u∫Σh(x)e2udVg − 1)−2π∑j=1mαj(δpj−1)(E) stated on a compact orientable Riemannian surface (Σ,g) with no boundary and Volg(Σ)=1. Here, ρ is a real parameter, α––=(α1,…,αm)∈(−1,0)m and the corresponding space of formal barycenters is defined as Σρ,α––=⎧⎩⎨∑qj∈Jtjδqj:J is finite, ∑qj∈Jtj=1, tj≥0, qj∈Σ,4πχ(J)
On the solvability of singular Liouville equations on compact surfaces of arbitrary genus / Carlotto, Alessandro. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 366:3(2014), pp. 1237-1256. [10.1090/s0002-9947-2013-05847-3]
On the solvability of singular Liouville equations on compact surfaces of arbitrary genus
Alessandro Carlotto
2014-01-01
Abstract
This paper deals with the singular Liouville equation −Δgu=ρ(h(x)e2u∫Σh(x)e2udVg − 1)−2π∑j=1mαj(δpj−1)(E) stated on a compact orientable Riemannian surface (Σ,g) with no boundary and Volg(Σ)=1. Here, ρ is a real parameter, α––=(α1,…,αm)∈(−1,0)m and the corresponding space of formal barycenters is defined as Σρ,α––=⎧⎩⎨∑qj∈Jtjδqj:J is finite, ∑qj∈Jtj=1, tj≥0, qj∈Σ,4πχ(J)File in questo prodotto:
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