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$C^{2,\alpha }$ estimate of a parabolic Monge-Ampère equation on $S^{n}$

Author: Dong-Ho Tsai
Journal: Proc. Amer. Math. Soc. 131 (2003), 3067-3074
MSC (2000): Primary 35K10, 58J35
Published electronically: February 6, 2003
MathSciNet review: 1993215
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Abstract: We consider a special type of parabolic Monge-Ampère equation on $S^{n}$arising from convex hypersurfaces expansion in Euclidean spaces. We obtained a $C^{2,\alpha }$ parabolic estimate of the support functions for the convex hypersurfaces assuming that we have already had a $C^{2}$parabolic estimate.

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Additional Information

Dong-Ho Tsai
Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu 300, Taiwan

Received by editor(s): August 2, 2001
Received by editor(s) in revised form: April 23, 2002
Published electronically: February 6, 2003
Additional Notes: This research was supported by NSC of Taiwan, Grant # 89-2115-M-194-026
Communicated by: Bennett Chow
Article copyright: © Copyright 2003 American Mathematical Society

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