Christoph Kopper, Volkhard F. M\"uller
Renormalization Proof for Massive $\vp_4^4$ Theory 
on Riemannian Manifolds
(142K, latex)

ABSTRACT.  In this paper we present an inductive renormalizability proof 
for massive $\vp_4^4$ theory on Riemannian manifolds, 
based on the Wegner-Wilson flow equations of the Wilson 
renormalization group, adapted to perturbation theory. 
The proof goes in hand with bounds on the perturbative Schwinger functions 
which imply tree decay between their position arguments. 
An essential prerequisite are precise bounds on the short and long distance 
behaviour of the heat kernel on the manifold. With the aid of a 
regularity assumption (often taken for granted) we also show, that 
for suitable renormalization conditions 
the bare action takes the minimal form, that is to say, there appear the 
same counter terms as in flat space, apart from a logarithmically 
divergent one which is proportional to the scalar curvature.