O geometrii laplasiánu. I
O geometrii laplasiánu. II
On a fourth order equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a Fourth Order Equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
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.
On a fully nonlinear Yamabe problem
On a Purely ?Riemannian" Proof of the Structure and Dimension of the Unramified Moduli Space of a Compact Riemann Surface.
On contact equivalence of holomorphic Monge-Ampére equations.
On Liouville theorem and apriori estimates for the scalar curvature equations
On metrics of positive Ricci curvature conformal to
Let be a closed Riemannian manifold and the Euclidean metric. We show that for , is not conformal to a positive Einstein manifold. Moreover, is not conformal to a Riemannian manifold of positive Ricci curvature, through a radial, integrable, smooth function, , for . These results are motivated by some recent questions on Yamabe constants.
On minimal hypersurfaces of nonnegatively Ricci curved manifolds.
On pseudo Ricci-symmetric manifolds.
On radius, systole, and positive Ricci curvature.
On related vector fields of capillary surfaces.
On Schrödinger maps from to
We prove an estimate for the difference of two solutions of the Schrödinger map equation for maps from to This estimate yields some continuity properties of the flow map for the topology of , provided one takes its quotient by the continuous group action of given by translations. We also prove that without taking this quotient, for any the flow map at time is discontinuous as a map from , equipped with the weak topology of to the space of distributions The argument relies in an essential...
On special Riemannian -manifolds with distinct constant Ricci eigenvalues
The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.
On the asymptotic behavior of Dirichlet problems in a riemannian manifold less small random holes
On the asymptotic geometry of gravitational instantons
We investigate the geometry at infinity of the so-called “gravitational instantons”, i.e. asymptotically flat hyperkähler four-manifolds, in relation with their volume growth. In particular, we prove that gravitational instantons with cubic volume growth are ALF, namely asymptotic to a circle fibration over a Euclidean three-space, with fibers of asymptotically constant length.
On the Conformal and CR Automorphism Groups.
On the Curvature and Heat Flow on Hamiltonian Systems
We develop the differential geometric and geometric analytic studies of Hamiltonian systems. Key ingredients are the curvature operator, the weighted Laplacian, and the associated Riccati equation.We prove appropriate generalizations of the Bochner-Weitzenböck formula and Laplacian comparison theorem, and study the heat flow.