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<p>Branched rough paths, used to solve ODEs on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>, have been generalised in two different directions. In one direction, there are regularity structures aimed at solving SPDEs on Euclidean spaces. In the other direction, there are planarly branched rough paths to solve ODEs on homogeneous spaces. This paper combines these two directions to construct planar regularity structures, for (S)PDEs on homogeneous spaces.</p>

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Planar Regularity Structures

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月8日

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  • Ludwig Rahm

摘要

Branched rough paths, used to solve ODEs on \(\mathbb {R}\) R , have been generalised in two different directions. In one direction, there are regularity structures aimed at solving SPDEs on Euclidean spaces. In the other direction, there are planarly branched rough paths to solve ODEs on homogeneous spaces. This paper combines these two directions to construct planar regularity structures, for (S)PDEs on homogeneous spaces.