Ray Transform on Riemannian Manifolds

2004 ◽  
pp. 187-259 ◽  
Author(s):  
Vladimir A. Sharafutdinov
Keyword(s):  
Riemannian Manifolds ◽  
Ray Transform

scholarly journals Mixed ray transform on simple $2$-dimensional Riemannian manifolds

2019 ◽  
Vol 147 (11) ◽  
pp. 4901-4913 ◽  
Author(s):  
Maarten V. de Hoop ◽  
Teemu Saksala ◽  
Jian Zhai
Keyword(s):  
Riemannian Manifolds ◽  
Ray Transform

scholarly journals A Reflection Approach to the Broken Ray Transform

2015 ◽  
Vol 117 (2) ◽  
pp. 231 ◽  
Author(s):  
Joonas Ilmavirta
Keyword(s):  
Riemannian Manifolds ◽  
Ray Transform ◽  
Partial Data ◽  
Manifolds With Corners ◽  
Geodesic Ray Transform

We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity results for the broken ray transform using corresponding earlier results for the geodesic ray transform. Examples of manifolds where the broken ray transform is injective include Euclidean cones and parts of the spheres $S^n$. In addition, we introduce the periodic broken ray transform and use the reflection argument to produce examples of manifolds where it is injective. We also give counterexamples to both periodic and nonperiodic cases. The broken ray transform arises in Calderón's problem with partial data, and we give implications of our results for this application.

On Ricci Riemannian Manifolds

2010 ◽  
Vol 0 (-1) ◽  
pp. 437-446 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Riemannian Manifolds

On the equicontinuity of families of inverse mappings of Riemannian manifolds

2019 ◽  
Vol 16 (4) ◽  
pp. 557-566
Author(s):  
Denis Ilyutko ◽  
Evgenii Sevost'yanov
Keyword(s):  
Riemannian Manifolds ◽  
Type Inequality ◽  
The Given ◽  
Range Of Values

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

Ball-homogeneous and disk-homogeneous Riemannian manifolds

1982 ◽  
Vol 180 (4) ◽  
pp. 429-444 ◽  
Author(s):  
Old?ich Kowalski ◽  
Lieven Vanhecke
Keyword(s):  
Riemannian Manifolds ◽  
Homogeneous Riemannian Manifolds

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Sign in / Sign up

Export Citation Format

Share Document