Calculus of Variations and Geometric Measure Theory

Morse theory and a scalar field equation on compact surfaces

Andrea Malchiodi (Scuola Normale Superiore)

created by abbondand on 26 Feb 2007

15 mar 2007


We consider an elliptic equation on compact surfaces with motivations from physics (Euler flows, Chern-Simons theory) or differential geometry (Gauss curvature, Q-curvature). Using a Morse-theoretical approach we improve some existence results in the literature which were based on blow-up analysis, and derive a simple and direct proof of a known degree-counting formula for the equation.