Related papers: Bol's type inequality for singular metrics and its…
For dimensions $n \geq 3$, we classify singular solutions to the generalized Liouville equation $(-\Delta)^{n/2} u = e^{nu}$ on $\mathbb{R}^n \setminus \{0\}$ with the finite integral condition $\int_{\mathbb{R}^n} e^{nu} < \infty$ in terms…
In the conformal class of Euclidean space, we give some volume comparison theorems with help of Q-curvature. Meanwhile, for compact four dimensional manifolds with non-negative scalar curvature, we give a volume rigidity theorem with…
This paper is devoted to the Q-curvature type equation with singularities; mainly we give existence and regularity results of solutions. To have positive solutions which will be meaningfully in conformal geometry we restrict ourself to…
In this short note, we study the smoothness of the extremal solutions to the Liouville system
This paper is devoted to the construction of weak solutions to the singular constant $Q$-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of…
On $(M,g)$ a compact riemannian $4-$manifold we consider the prescribed $Q-$curvature equation defined on $M$ with finite singular sources. We first prove a classification theorem for singular Liouville equations defined on $\mathbb R^4$…
We obtain a generalized version of an inequality, first derived by C. Bandle in the analytic setting, for weak subsolutions of a singular Liouville-type equation. As an application we obtain a new proof of the Alexandrov isoperimetric…
We give necessary and sufficient conditions for the existence of positive radial solutions for a class of fully nonlinear uniformly elliptic equations posed in the complement of a ball in $\mathbb R^N$, and equipped with homogeneous…
We establish two comparison results between the solutions of a class of mean curvature equations and pieces of arcs of circles that satisfy the same Neumann boundary condition. Finally we present a number of examples where our estimates can…
In this paper we classify the solutions to the geometric Neumann problem for the Liouville equation in the upper half-plane or an upper half-disk, with the energy condition given by finite area. As a result, we classify the conformal…
The paper concerns the solvability by quadratures of linear differential systems, which is one of the questions of differential Galois theory. We consider systems with regular singular points as well as those with (non-resonant) irregular…
We prove some general results on the existence and uniqueness of solutions to the Liouville equation. Then, we discuss the sharpness and possible generalizations. Finally, we give several applications, arising in both mathematics and…
In this paper, we prove uniqueness of solutions of mean field equations with general boundary conditions for the critical and subcritical total mass regime, extending the earlier results for null Dirichlet boundary condition. The proof is…
We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.
In this paper, we will use the normalized intetral Ricci curvature to investigate Liouville type property of $ p $ harmonic function on Riemannian manifold. secondly, we will use the BiRic curvature to obtian Liuville theorem for $ p $…
Given a compact four dimensional manifold, we prove existence of conformal metrics with constant $Q$-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure.…
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to discuss the global existence and uniqueness results for fractional differential equations of Riemann-Liouville type. Some…
We present a simple analytic bound on the quantum value of general correlation type Bell inequalities, similar to Tsirelson's bound. It is based on the maximal singular value of the coefficient matrix associated with the inequality. We…
In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.