On the compactness of isometry groups in complex analysis 

 - Bangalore:  Department of Mathematics, Indian Institute of Science:  2006 
 - We prove that the group of continuous isometries for the Kobayashi or Carath´eodory metrics of a strongly convex domain in Cn is compact unless the domain is biholomorphic to the ball. A key ingredient, proved using differential geometric ideas, is that a 
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