The globally homeomorphic solutions to Beltrami system in Cn.
The local structure of Nodal set of solutions of Schrödinger equation on Riemannian 3-manifolds.
The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with addititonal conditions on compact subsets.
The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets
The second Yamabe invariant with singularities
Let be a compact Riemannian manifold of dimension .We suppose that is a metric in the Sobolev space with and there exist a point and such that is smooth in the ball . We define the second Yamabe invariant with singularities as the infimum of the second eigenvalue of the singular Yamabe operator over a generalized class of conformal metrics to and of volume . We show that this operator is attained by a generalized metric, we deduce nodal solutions to a Yamabe type equation with...
The spectra and the symmetric structure on a compact symmetric space.
Transition operators on co-compact G-spaces.
We develop methods for studying transition operators on metric spaces that are invariant under a co-compact group which acts properly. A basic requirement is a decomposition of such operators with respect to the group orbits. We then introduce reduced transition operators on the compact factor space whose norms and spectral radii are upper bounds for the Lp-norms and spectral radii of the original operator. If the group is amenable then the spectral radii of the original and reduced operators coincide,...