Limits of Solutions to a Parabolic Monge-Ampere Equation
| dc.creator | Loftin, John | |
| dc.creator | Tsui, Mao-Pei | |
| dc.date | 2008-02-01 | |
| dc.date.accessioned | 2026-07-07T09:18:26Z | |
| dc.date.available | 2026-07-07T09:18:26Z | |
| dc.description | We present the results from our earlier paper (arXiv:math/0602484) on the affine normal flow on noncompact convex hypersurfaces in affine space from a more PDE point of view, emphasizing the estimates involved. Our results concern the limits of solutions to a parabolic Monge-Ampere equation on $S^n$, where a sequence of smooth strictly convex initial value functions increase monotonically to a limiting initial value function which is infinite on at least a hemisphere of $S^n$. We prove long-time existence and instantaneous smoothing for quite general initial data, and we characterize ancient solutions as ellipsoids or paraboloids. We make essential use of estimates of Andrews and Gutierrez-Huang, and barriers due to Calabi. | |
| dc.identifier | https://arxiv.org/abs/0802.0208 | |
| dc.identifier | http://arxiv.org/abs/0802.0208 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154021 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35K55; 53A15; 53C44 | |
| dc.title | Limits of Solutions to a Parabolic Monge-Ampere Equation | |
| dc.type | text |