TY - JOUR
T1 - The Kähler-Ricci flow on hirzebruch surfaces
AU - Song, Jian
AU - Weinkove, Ben
PY - 2011/10
Y1 - 2011/10
N2 - 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 P1 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.
AB - 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 P1 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.
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U2 - 10.1515/CRELLE.2011.071
DO - 10.1515/CRELLE.2011.071
M3 - Article
AN - SCOPUS:80053624031
SN - 0075-4102
SP - 141
EP - 168
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 659
ER -