On conformal maps with starlike images.

Conformal and Harmonic Measures on Laminations Associated with Rational Maps

The framework of aane and hyperbolic laminations provides a unifying foundation for many aspects of conformal dynamics and hyperbolic geometry. The central objects of this approach are an aane Riemann surface lamination A and the associated hyperbolic 3-lamination H endowed with an action of a discrete group of iso-morphisms. This action is properly discontinuous on H, which allows one to pass ...

On Discrete Conformal Seamless Similarity Maps

An algorithm for the computation of global discrete conformal parametrizations with prescribed global holonomy signatures for triangle meshes was recently described in [Campen and Zorin 2017]. In this paper we provide a detailed analysis of convergence and correctness of this algorithm. We generalize and extend ideas of [Springborn et al. 2008] to show a connection of the algorithm to Newton’s ...

Conformal Maps and Minimal Surfaces

Quadratic Maps with Convex Images

Seeking exactness for \convex relaxation", we deene a map f : < n ! < m to be ICON if its image f(< n) is convex. Analogously, f is termed LICON(AICON) if the image of every linear (every aane) vsubspace under f is convex. In this paper, we investigate quadratic maps of these three types. These maps are motivated by a fact shown here that they prescribe conditions under which feasibility and op...

Conformal maps and non-reversibility of elliptic area-preserving maps

It has been long observed that area-preserving maps and reversible maps share similar results. This was certainly known to G.D. Birkhoff [5] who showed that these two types of maps have periodic orbits near a general elliptic fixed point. The KAM theory, developed by Kolmogorov-ArnoldMoser for Hamiltonian systems [9], [1] and area preserving maps [15], has also been extended a great deal to rev...