For Liouville equations with singular sources, the interpretation of the equation and its
impact are most significant if the singular sources are quantized: the strength of each Dirac …

The present survey is devoted to results on Trudinger-Moser inequalities in two dimension.
We give a brief overview of the history of these celebrated inequalities and, starting from the …

For singular mean field equations defined on a compact Riemann surface, we prove the
uniqueness of bubbling solutions as far as blowup points are either regular points or non …

We prove the uniqueness of blow up solutions of the mean field equation as ρ n→ 8 π m,
m∈ N. If un, 1 and un, 2 are two sequences of bubbling solutions with the same ρ n and the …

On strictly starshaped domains of second kind (see Definition 1.2) we find sufficient
conditions which allow the solution of two long standing open problems closely related to …

In this article we describe the system of point vortices, derived by Helmholtz from the Euler
equation, and their associated Gibbs measures. We discuss solution concepts and available …

We derive a singular version of the Sphere Covering Inequality which was recently
introduced in Gui and Moradifam (Invent Math. https://doi. org/10.1007/s00222-018-0820-2 …

Full article: Local uniqueness of m-bubbling sequences for the Gel’fand equation Skip to Main
Content Taylor and Francis Online homepage Taylor and Francis Online homepage Log in …

The aim of this paper is to complete the program initiated in [51],[23] and then carried out by
several authors concerning non-degeneracy and uniqueness of solutions to mean field …

We establish the non-degeneracy of bubbling solutions for singular mean field equations
when the blow-up points are either regular or non-quantized singular sources. This extends …