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The main idea for our approach relies on a study of the boundary theory we established for the general CAT(-1) spaces.
      
LetD be a Hermitian symmetric space of tube type,S its Shilov boundary andG the neutral component of the group of bi-holomorphic diffeomorphisms ofD.
      
Taking a specific determination of its argument and studying its limit when approaching the Shilov boundary, we are able to define a ?-valued,G-invariant kernel for triples of mutually transversal points inS.
      
For every orbitGυ which is not polynomially convex we construct an analytic annulus or strip inG?υ with the boundary inGυ.
      
Such properties are expressed using the Furstenberg boundary of the associated symmetric space ? × ?.
      
Orbits of triples in the Shilov boundary of a bounded symmetric domain
      
A necessary and sufficient geometric condition on the growth of the boundary of approximate tiles is reduced to a problem in Fourier analysis that is shown to have an elegant simple solution in dimension one.
      
We show that D is uniquely determined from boundary measurements corresponding two appropriately chosen Neumann datas.
      
The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
      
Behavior near the boundary of positive solutions of second order parabolic equations
      
Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure
      
Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for carnot-carathéodory metrics
      
On boundary behavior of harmonic functions in H?lder domains
      
We analyze the boundary behavior of harmonic functions in a domain whose boundary is locally given by a graph of a H?lder continuous function.
      
We prove that the boundary of a bounded domain is a set of injectivity for the twisted spherical means on ?n for a certain class of functions on ?n.
      
By producing a L2 convergent Neumann series, we prove the invertibility of the elastostatics and hydrostatics boundary layer potentials on arbitrary Lipschitz domains with small Lipschitz character and 3D polyhedra with large dihedral angles.
      
Boundary-variation solution of eigenvalue problems for elliptic operators
      
We present an algorithm which, based on certain properties of analytic dependence, constructs boundary perturbation expansions of arbitrary order for eigenfunctions of elliptic PDEs.
      
 

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