# 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

- Physics
- 2010

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

- MathematicsProceedings 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

- Mathematics
- 2016

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

- Physics
- 2010

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

- Physics, Mathematics
- 2017

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

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Conformal maps on Hilbert space

- Mathematics
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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