The existence criterion of holomorphic discs for higher A_∞ operations via minimal discs

2026/04/30 by Qiang Tan, Zuyi Zhang · 1 voice
Mathematics · #math.SG #math.CV #math.DG

paper · pdf

Abstract

The main theorem of the paper provides an existence criterion of holomorphic discs for higher A_∞ operations. The key step is to show that if a minimal disc in a Kähler 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 \CP^m with boundary on \RP^m are holomorphic.

Citations

• Holomorphic disks with boundary on compact Lagrangian surface
• Construction of holomorphic quilts in Cartesian product of closed surfaces
• SYZ transforms for immersed Lagrangian multi-sections
• Floer cohomology of the Chiang Lagrangian
• Lectures on Minimal Surface Theory
• A beginner's introduction to Fukaya categories
• The Maslov index for paths
• Pseudo holomorphic curves in symplectic manifolds
• Compact k�hler manifolds of positive bisectional curvature
• Morse theory for Lagrangian intersections

Discussions

• Qiang Tan, Zuyi Zhang: The existence criterion of holomorphic discs for higher $A_\infty$ operations via minimal discs https://arxiv.org/abs/2604.27778 https://arxiv.org/pdf/2604.27778 https://arxiv.o [bsky, 0 points, 0 comments]

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