5,038 research outputs found
On the injectivity of the circular Radon transform arising in thermoacoustic tomography
The circular Radon transform integrates a function over the set of all
spheres with a given set of centers. The problem of injectivity of this
transform (as well as inversion formulas, range descriptions, etc.) arises in
many fields from approximation theory to integral geometry, to inverse problems
for PDEs, and recently to newly developing types of tomography. The article
discusses known and provides new results that one can obtain by methods that
essentially involve only the finite speed of propagation and domain dependence
for the wave equation.Comment: To appear in Inverse Problem
Regularity of Kobayashi metric
We review some recent results on existence and regularity of Monge-Amp\`ere
exhaustions on the smoothly bounded strongly pseudoconvex domains, which admit
at least one such exhaustion of sufficiently high regularity. A main
consequence of our results is the fact that the Kobayashi pseudo-metric k on an
appropriare open subset of each of the above domains is actually a smooth
Finsler metric. The class of domains to which our result apply is very large.
It includes for instance all smoothly bounded strongly pseudoconvex complete
circular domains and all their sufficiently small deformations.Comment: 14 pages, 8 figures - The previously announced main result had a gap.
In this new version the corrected statement is given. To appear on the volume
"Geometric Complex Analysis - Proceedings of KSCV 12 Symposium
Pluripolar hulls and fine analytic structure
We discuss the relation between pluripolar hulls and fine analytic structure.
Our main result is the following. For each non polar subset of the complex
plane we prove that there exists a pluripolar set with the property that the pluripolar hull of relative
to contains no fine analytic structure and its projection onto
the first coordinate plane equals .Comment: 14 pages, revised version, to appear in Indagationes Mathematica
Intersection of valuation rings in
We associate to any given finite set of valuations on the polynomial ring in
two variables over an algebraically closed field a numerical invariant whose
positivity characterizes the case when the intersection of their valuation
rings has maximal transcendence degree over the base fields.
As an application, we give a criterion for when an analytic branch at
infinity in the affine plane that is defined over a number field in a suitable
sense is the branch of an algebraic curve
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