Numerical conformal mapping and analytic continuation

Analytic Continuation in Mapping Spaces

We consider a Stein manifold M of dimension ≥ 2 and a compact subset K ⊂ M such that M ′ = M\K is connected. Let S be a compact differential manifold, and let MS , resp. M ′ S stand for the complex manifold of maps S → M , resp. S → M , of some specified regularity that are homotopic to constant. We prove that any holomorphic function on M ′ S continues analytically to MS (perhaps as a multival...

Analytic Continuation of a Biholomorphic Mapping

0. Introduction and Preliminary 2 0.1. Existence and uniqueness theorem 2 0.2. Equation of a chain 7 1. Nonsingular matrices 9 1.1. A family of nonsingular matrices 9 1.2. Sufficient condition for Nonsingularity 12 1.3. Estimates 16 2. Local automorphism group of a real hypersurface 23 2.1. Polynomial Identities 23 2.2. Injectivity of a Linear Mapping 33 2.3. Beloshapka-Loboda Theorem 42 3. Com...

Numerical analytic continuation of holomorphic functions in Cn

Geometric trajectory filtering via numerical conformal mapping

The paper studies the problem which we refer to as geometric trajectory filtering, where only trajectories that satisfy the local safety constraints are selected from a library of trajectories. The goal is to speed up primitive-based motion planning while still maintaining a relatively a large collection of motion primitives. One way to solve this problem is to obtain a proper (preferably smoot...

Green currents and analytic continuation