We compute the$L$^{$p$}-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds.
Using rearrangements of matrix-valued sequences, we prove that with certain boundary conditions the solution of the one-dimensional Schrödinger equation increases or decreases under monotone rearrangements of its potential.
Sergey IvashkovichDépartement de Mathématiques, Université Lille ISergey PinchukDepartment of Mathematics, Indiana UniversityJean-Pierre RosayDepartment of Mathematics, University of Wisconsin
It is well known that every Hölder continuous function on the unit circle is the sum of two functions such that one of these functions extends holomorphically into the unit disc and the other extends holomorphically into the complement of the unit disc. We prove that an analogue of this holds for Hölder continuous functions on an annulus A which have zero averages on all circles contained in A which surround the hole.