A Monotonicity Formula for the Extrinsic Biharmonic Map Heat Flow

Elena M\"ader-Baumdicker; Nils Neumann

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A Monotonicity Formula for the Extrinsic Biharmonic Map Heat Flow

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arxiv 2504.06089 v1 pith:CK52UYMO submitted 2025-04-08 math.DG math.AP

Elena Mäder-Baumdicker , Nils Neumann This is my paper · ORCID

classification math.DGmath.AP

keywords biharmonicheatextrinsicflowmonotonicitybehaviorsderiveentropy

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abstract

We explore novel properties of the biharmonic heat kernel on Euclidean space and derive an entropy type quantity for the extrinsic biharmonic map heat flow which exhibits monotonicity behaviors for $n\leq 4$.

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