Some questions on integral geometry on Riemannian manifolds (Q2736867)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Some questions on integral geometry on Riemannian manifolds |
scientific article; zbMATH DE number 1644970
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some questions on integral geometry on Riemannian manifolds |
scientific article; zbMATH DE number 1644970 |
Statements
11 September 2001
0 references
averages of integrable functions
0 references
NA-sets
0 references
0 references
0.9032241
0 references
0.9012559
0 references
0.8927296
0 references
Some questions on integral geometry on Riemannian manifolds (English)
0 references
Let \(M\) be a complete real-analytic Riemannian manifold with sectional curvatures bounded from above and below. A non-empty set \(\Gamma\subset M\) is a NA-set if the only real-analytic function defined on a neighborhood of \(\Gamma\) which vanishes identically on \(\Gamma\) is the zero function. The authors prove that a measurable function defined on M is determined by its averages on all superisothermal sets centred at points belonging to a NA-set. This extends known results on spherical averages of locally integrable functions in Euclidean space.
0 references
