Geometric PDE Seminar

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.