Tetra and Didi, the cosmic spectral twins.
The abstract Riemannian path space.
The almost Einstein operator for distributions
For the geometry of oriented distributions , which correspond to regular, normal parabolic geometries of type for a particular parabolic subgroup , we develop the corresponding tractor calculus and use it to analyze the first BGG operator associated to the -dimensional irreducible representation of . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions of this operator...
The analytic Carathéodory conjecture.
The asymptotic behavior of Green's functions for degenerating hyperbolic surfaces.
The Atiyah-Patodi-Singer theorem for perturbed Dirac operators on even-dimensional manifolds with bounded geometry.
The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs.
The -pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
The behaviour of the Gaussian beam in an anisotropic medium with an interface between two media.
The Bochner Laplacian, Riemannian submersions, heat content asymptotics, and heat equation asymptotics
The bottom of the spectrum of a Riemannian covering.
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The boundary-contact problem of elasticity for homogeneous anisotropic media with a contact on some part of the boundaries.
The Cauchy problem for Lorentz metrics with prescribed Ricci curvature
The Cauchy problem for systems through the normal form of systems and theory of weighted determinant
The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and well-posedness (Levi condition).
The Cauchy problem with logarithmic ramifications for -modules
The cohomology solution and the index theorem on ring surfaces of genus .
The cokernel of the operator acting on a -module, II
The configuration space integral for links in .
The CR Yamabe conjecture the case
Let be a compact CR manifold of dimension with a contact form , and its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form on conformal to which has a constant Webster curvature. This problem is equivalent to the existence of a function such that , on . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where and is not locally CR equivalent to the sphere of . In a join work with R. Yacoub, the CR Yamabe problem...