CORDIS Project
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This project seeks to develop a theoretical framework for understanding Hele-Shaw flow and its connections to geodesic rays in Kähler metrics. By applying techniques from the study of holomorphic curves, the research aims to enhance insights into regularity and singularities in these mathematical contexts.
Very recently Dr.
Julius Ross at the Univ. of Cambridge and I found a striking connection between geodesic rays in spaces of Kähler metrics and the Hele-Shaw flow (Laplacian growth).
By this connection both have a similar interpretation as certain families of embedded holomorphic curves attached along their boundaries to a Lagrangian submanifold.The first objective is to develop the regularity theory of the Hele-Shaw flow (Laplacian growth) using techniques from the theory of moduli spaces of em…
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