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arXiv · 2603.01832

Fueter equations and the search for a higher dimensional Hamiltonian Floer theory I: analytical foundations and compactness

L. Asselle·R. Brilleslijper
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Abstract

We study a Floer-theoretic approach to harmonic maps from the two-torus into non-flat K\"ahler manifolds. Building on the complex-regularized polysymplectic (CRPS) formalism of [BF24], which provides a Hamiltonian description of harmonic maps for which the associated equations are elliptic, we analyze the compactness of the associated moduli spaces of Fueter maps. For compact quotients $Q$ of complex hyperbolic space, we exploit the structure of the Biquard-Gauduchon hyperk\"ahler metric to prove relative compactness under suitable smallness assumptions on the Hamiltonian. In the flat case, we establish the necessary quantitative $L^\infty$-estimates and outline a perturbative strategy for the non-flat setting.

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L. Asselle, R. Brilleslijper. 2026-03-02. Fueter equations and the search for a higher dimensional Hamiltonian Floer theory I: analytical foundations and compactness. https://arxiv.org/abs/2603.01832

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