# Inversion theory and conformal mapping

```@inproceedings{Blair2000InversionTA,
title={Inversion theory and conformal mapping},
author={David Ervin Blair},
year={2000}
}```
Classical inversion theory in the plane Linear fractional transformations Advanced calculus and conformal maps Conformal maps in the plane Conformal maps in Euclidean space The classical proof of Liouville's theorem When does inversion preserve convexity? Bibliography Index.
102 Citations
Conformal Mapping of Relativistic Quantum Bound Systems to Eliminate Potential Fields
In two recent papers, an isometric conformal transformation has been introduced that eliminates potential interaction terms from the Schrodinger equation for central potential problems. The method
Uniqueness theorems of self-conformal solutions to inverse curvature flows
• Mathematics
Proceedings of the American Mathematical Society
• 2020
It has been known in that round spheres are the only closed homothetic self-similar solutions to the inverse mean curvature flow and parabolic curvature flows by degree -1 homogeneous functions of
Cartan-Fubini Type Extension Theorems
Liouville’s theorem in conformal geometry can be generalized to extension problems of holomorphic maps preserving certain structures on Fano manifolds. The most typical result of this type is
On Inverse Surfaces in Euclidean 3-Space
• Mathematics
• 2012
In this paper, we study the inverse surfaces in 3-dimensional Euclidean space \$\mathbb{E}^{3}\$. We obtain some results relating Christoffel symbols, the normal curvatures, the shape operators and the
ON THE NON-EXISTENCE OF ZERO MODES
• Physics, Mathematics
• 2018
We consider magnetic fields on R3 which are parallel to a conformal Killing field. When the latter generates a simple rotation we show that a Weyl–Dirac operator with such a magnetic field cannot
Conformal Transformation of the Schrödinger Equation for the Harmonic Oscillator into a Simpler Form
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation
On the non-existence of zero modes
We consider magnetic fields on \$\mathbb{R}^3\$ which are parallel to a conformal Killing field. When the latter generates a simple rotation we show that a Weyl-Dirac operator with such a magnetic
Weierstrass representations for triply orthogonal and conformal Euclidean and Lorentzian systems
• Mathematics
• 2020
Starting with triply orthogonal moving frames in 3-dimensional Lie algebras, we build Weierstrass representations for triply orthogonal and conformal coordinate systems in Euclidean and Lorentian
ON K-CONTACT EINSTEIN MANIFOLDS
• Mathematics
• 2016
In this paper, we investigate K-contact Einstein manifolds satisfying the conditions RC = Q(S,C), where C is the conformal curvature tensor and R the Riemannian curvature tensor. Next we consider

## References

SHOWING 1-3 OF 3 REFERENCES
Conformal maps on Hilbert space
REMARKS, (i) The dimension of H must be > 3 because every holomorphic map on C with a nowhere zero derivative is conformai. (ii) For R, the theorem is known even for/just C [2]. (iii) The proof of
Coyle Lectures on contemporary probability
• 1999