Group contractions and conformal maps in nuclear structure

Conformal Maps and Minimal Surfaces

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...

Conformal Maps and p-Dirichlet Energies

Let Φ : (M1, g1)→ (M2, g2) be a diffeomorphism between Riemannian manifolds and Φ# : D(M2)→ D(M1) the induced pull-back operator. The main theorem of this work is Theorem 4.1 which relates preservation of the p-Dirichlet energies φ 7→ ∫ Mi |dφ| dμi under Φ# to isometric or conformal properties of Φ. More precisely: In case p = n, Φ# preserves the p-Dirichlet energy if and only if Φ is conformal...

Tree-like Decompositions and Conformal Maps

Any simply connected rectifiable domain Ω can be decomposed into uniformly chord-arc subdomains using only crosscuts of the domain. We show that such a decomposition allows one to construct a map from Ω to the disk which is close to conformal in a uniformly quasiconformal sense. This answers a question of Stephen Vavasis. 1991 Mathematics Subject Classification. Primary: 30C35 Secondary: 30C30,...

Conformal Maps and Dispersionless Integrable Hierarchies

We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy singled out by the conditions known as ”string equations”. The same hierarchy locally solves the 2D inverse potential problem, i.e., reconstruction of the d...