MATH Seminar
| Title: A characterization of the polarity transform for reflectors |
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| Seminar: Analysis and Differential Geometry |
| Speaker: Anastasia Svishcheva of Emory University |
| Contact: Vladimir Oliker, oliker@mathcs.emory.edu |
| Date: 2011-10-04 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: Convex reflectors arise as solutions to nonlinear second order elliptic partial differential equations (PDE's) of Monge-Amp\`{e}re type expressing conservation laws in geometrical optics. Previously it was shown by V. Oliker that this transform can be viewed as duality with respect to the form $Q(X,Y):=|X||Y|-\langle X, Y \rangle,~X, Y \in \mathbb{R}^{n+1}$. A natural and interesting geometric question is to find a minimal set of properties characterizing such duality transform between reflectors. I will speak about sufficient conditions for this transformation to be such duality. |
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