2019/04/26 by Weonmo Lee, Lee, Weonmo, Yong‐Geun Oh +4
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.SG
paper · pdf · doi:10.48550/arxiv.1904.11775
24 pages, 7 figures;v2) typos corrected, English improved, More references added;v3) 32 pages, 16 figures, the third author newly added, previous main theorem improved, density question resolved and many more results on relative ball packings added
openalex publication_date 2019/04/26 · openalex created_date 2019/05/03 · arxiv created 2019/06/14 · arxiv updated 2019/06/17 · openalex updated_date 2026/07/28
In this paper, we study various asymptotic behavior of the infinite family of monotone Lagrangian tori Ta,b,c in \mathbbCP2 associated to Markov triples (a,b,c) described in \citeVi14. We first prove that the Gromov capacity of the complement \mathbbCP2 ∖ Ta,b,c is greater than or equal to \frac13 of the area of the complex line for all Markov triple (a,b,c). We then prove that there is a representative of the family \Ta,b,c\ whose loci completely miss a metric ball of nonzero size and in particular the loci of the union of the family is not dense in \mathbbCP2.