Remark on some conformally invariant integral equations: the method of moving spheres
Continuity of solutions of uniformly elliptic equations in R2.
Nonexistence of axially symmetric, stationary solution of Einstein vacuum equation with disconnected symmetric event horizon.
A Liouville theorem for solutions of the Monge–Ampère equation with periodic data
A note on the Kazdan-Warner type condition
On a min-max procedure for the existence of a positive solution for certain scalar field equations in R.
In this paper we mainly introduce a min-max procedure to prove the existence of positive solutions for certain semilinear elliptic equations in R.
A geometric problem and the Hopf Lemma. I
A classical result of A. D. Alexandrov states that a connected compact smooth -dimensional manifold without boundary, embedded in , and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of in a hyperplane in case satisfies: for any two points , on , with , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional condition for . Some variations...
A fully nonlinear version of the Yamabe problem on manifolds with boundary
We propose to study a fully nonlinear version of the Yamabe problem on manifolds with boundary. The boundary condition for the conformal metric is the mean curvature. We establish some Liouville type theorems and Harnack type inequalities.
On a fractional Nirenberg problem. Part I: Blow up analysis and compactness of solutions
We prove some results on the existence and compactness of solutions of a fractional Nirenberg problem. The crucial ingredients of our proofs are the understanding of the blow up profiles and a Liouville theorem.
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