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arXiv · 2604.27778

The existence criterion of holomorphic discs for higher $A_\infty$ operations via minimal discs

Qiang Tan·Zuyi Zhang
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Abstract

The main theorem of the paper provides an existence criterion of holomorphic discs for higher $A_\infty$ operations. The key step is to show that if a minimal disc in a K\"ahler manifold with boundary in a sequence of Lagrangian submanifolds intersecting transversely such that its partial Maslov indices are either all no less than $1$ or all no larger than $-1$, then there is a holomorphic disc with the same image as this minimal disc. As a by-product, we show that all minimal discs in $\C\mathrm{P}^m$ with boundary on $\R\mathrm{P}^m$ are holomorphic.

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Qiang Tan, Zuyi Zhang. 2026-04-30. The existence criterion of holomorphic discs for higher $A_\infty$ operations via minimal discs. https://arxiv.org/abs/2604.27778

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