Harmonic Maps to Buildings and Singular Perturbation Theory

Spectral Networks and Harmonic Maps to Buildings

Constructing Buildings and Harmonic Maps

In a continuation of our previous work [20], we outline a theory which should lead to the construction of a universal pre-building and versal building with a φ-harmonic map from a Riemann surface, in the case of two-dimensional buildings for the group SL3. This will provide a generalization of the space of leaves of the foliation defined by a quadratic differential in the classical theory for S...

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory

Harmonic Maps with Fixed Singular Sets

§ 0. Introduction Here, for a smooth domain Ω in R and a compact smooth Riemannian manifold N we study a space H consisting of all harmonic maps u : Ω → N that have a singular set being a fixed compact subset Z of Ω having finite m− 3 dimensional Minkowski content. This holds if, for example, Z is m− 3 rectifiable [F, 3.2.14]. We define a suitable topology on H using Hölder norms on derivatives...