EXISTENCE RESULT FOR THE MEAN FIELD PROBLEM ON RIEMANN SURFACES OF ALL GENUSES

By Z. Djadli. 2008

127 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/732bb586e1791add440418b5826353ac6bfee72a

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Blow-up analysis of a Finsler–Liouville equation in two dimensions☆ (2012, background): “(2) have been intensively studied by many mathematicians, for there are many applications in geometric and physical problems, for example, in the problem of prescribing Gaussian curvature [9,12, 8], in the theory of the mean field equation [16,17,10,11,19,32] and in the Chern–Simons theory [38, 41,1”
Weighted barycentric sets and singular Liouville equations on compact surfaces (2011, methodology): “By means of all these tools, Djadli [23] was finally able to prove the solvability of (1) for ρ ∈ (4kπ, 4 (k + 1)π).”
An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, methodology): “As we will try to describe, our approach combines the scaling invariance properties in [53] and the possibility of volume concentration at multiple points (as in [34], [35]).”
Supercritical conformal metrics on surfaces with conical singularities (2011, unknown): “9 of [23].”
Some existence results for the Toda system on closed surfaces (2007, methodology): “sublevels {I L} (with L large) into k. By non-triviality we mean that this map is homotopically non-trivial, and indeed for any L > 0 there exists a map ’ : k ! {I L} (see (26) for the explicit formula, and Proposition 4.1 in [ 13 ] for the evaluation of I ) such that k ’ is homotopic to the identit”
Constant Q-curvature metrics in arbitrary dimension (2007, methodology): “Recently it has been used by Djadli in [ 24 ] to study a mean field equation depending on a real parameter ‚, and prove existence of solutions when ‚ 6= k8… without any assumption on the topology on the surface.”