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Abstract
We investigate the metric behavior of the Kähler–Ricci flow on the Hirzebruch surfaces, assuming the initial metric is invariant under a maximal compact subgroup of the automorphism group. We show that, in the sense of Gromov–Hausdorff, the flow either shrinks to a point, collapses to 
or contracts an exceptional divisor, confirming a conjecture of Feldman–Ilmanen–Knopf. We also show that similar behavior holds on higher-dimensional analogues of the Hirzebruch surfaces.
Received: 2009-05-07
Revised: 2010-05-18
Published Online: 2011-04-14
Published in Print: 2011-October
© Walter de Gruyter Berlin · New York 2011
