Geometric descriptions of the Loewner energy
48 mins 39 secs,
139.91 MB,
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About this item
| Description: |
Wang, Y
Tuesday 17th July 2018 - 13:45 to 14:30 |
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| Created: | 2018-07-17 16:01 |
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| Collection: | RGM follow up |
| Publisher: | Isaac Newton Institute |
| Copyright: | Wang, Y |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | The Loewner energy of a simple loop on the Riemann sphere is defined to be the Dirichlet energy of its driving function which is reminiscent in the SLE theory. It was shown in a joint work with Steffen Rohde that the definition is independent of the parametrization of the loop, therefore provides a Moebius invariant quantity on free loops which vanishes only on the circles. In this talk, I will present intrinsic interpretations of the Loewner energy (without involving the iteration of conformal distortions given by the Loewner flow), using the zeta-regularizations of determinants of Laplacians and show that the class of finite energy loops coincides with the Weil-Petersson class of the universal Teichmueller space. |
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