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SLE loop measures
SPEAKER  |  Dapeng Zhan
DATE  |  May 8(Mon), 2017
TIME  |  16:05
PLACE  |  1503
Keyword  |  
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ABSTRACT  |  We use Minkowski content (i.e., natural parametrization) of SLE to construct several types of SLEリリ loop measures for リ#(0,8)リ#(0,8). First, we construct rooted SLEリリ loop measures in the Riemann sphere ?? C^, which satisfy M?bius covariance, conformal Markov property, reversibility, and space-time homogeneity, when the loop is parameterized by its (1+リ8)(1+リ8)-dimensional Minkowski content. Second, by integrating rooted SLEリリ loop measures, we construct the unrooted SLEリリ loop measure in ?? C^, which satisfies M?bius invariance and reversibility. Third, we extend the SLEリリ loop measures from ?? C^ to subdomains of ?? C^ and to two types of Riemann surfaces using Brownian loop measures, and obtain conformal invariance or covariance of these measures. Finally, using a similar approach, we construct SLEリリ bubble measures in simply/multiply connected domains rooted at a boundary point. The work answers a question raised by Greg Lawler.
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