Liouville and logarithmic actions in Laplacian growth

2005/07/08 by Alexander Vasil’ev, Alexander Vasil'ev, Vasil'ev, Alexander
Mathematics · Physics and Astronomy · #76D27 #81T40 #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.MP #msc:76D27 #msc:81T40

paper · pdf · doi:10.48550/arxiv.math-ph/0507025

22 pages

arxiv created 2005/07/08 · openalex publication_date 2005/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss and construct an action functional (logarithmic action) for the simply connected Laplacian growth and obtain its variation. This variation admits various interpretations. In particular, we consider a general smooth subordination evolution and give connections with the Virasoro algebra and Neretin polynomials.

Citations

• Weil-Petersson metric on the universal Teichmuller space I: Curvature properties and Chern forms
• Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping
• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid

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