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Multiple SLE and the complex Burgers equation
Author(s) -
del Monaco Andrea,
Schleißinger Sebastian
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500230
Subject(s) - mathematics , limit (mathematics) , burgers' equation , infinity , mathematical analysis , boundary (topology) , vector field , limit point , field (mathematics) , point (geometry) , partial differential equation , pure mathematics , geometry
In this note we ask whether one can take the limit of multiple SLE as the number of slits goes to infinity. In the special case of n slits that connect n points of the boundary to one fixed point, one can take the limit of the Loewner equation that describes the growth of those slits in a simultaneous way. In this case, the limit is a deterministic Loewner equation whose vector field is determined by a complex Burgers equation.
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