|GEOMETRIC PDE SEMINAR|
|Topic:||Asymptotic Curvature Decay of Bach-Flat Metrics|
|Date:||Tuesday, February 10|
|Time/Room:||2:00pm - 3:00pm/S-101|
In pioneering work Tian/Viaclovsky initiated the study of the moduli space of Bach-flat metrics. They showed C^0-orbifold regularity and, equivalently, ALE order zero of noncompact finite-energy solutions. By use of Kato inequalities, the full smooth orbifold regularity was obtained by showing faster decay of Bach-flat ALE spaces in certain special cases such as harmonic curvature and extremal K\"ahler. Using a general technique of Cheeger-Tian we obtain faster decay in the general case.