The Donaldson geometric flow is a local smooth semiflow

2015/12/31 by Robin S. Krom, Krom, Robin S.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.1512.09199

arxiv created 2015/12/31 · openalex publication_date 2015/12/31 · arxiv updated 2016/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the local existence of unique smooth solutions of the Donaldson geometric flow on the space of symplectic forms on a closed smooth four-manifold, representing a fixed cohomology class. It is a semiflow on the Besov space B^1,p₂(M, Λ²) for p > 4. The Donaldson geometric flow was introduced by Simon Donaldson in [2]. For a detailed exposition see [6].

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