Teichmüller disks with small limit sets in PMF

2025/09/30 by Anna Lenzhen, Lenzhen, Anna
Chemistry · Mathematics · #57K20 #Analytic and geometric function theory #Chemical synthesis and pharmacological studies #FOS: Mathematics #Geometric Topology (math.GT) #Synthesis and Reactivity of Sulfur-Containing Compounds

paper · pdf · doi:10.48550/arxiv.2510.00286

openalex publication_date 2025/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study limit sets of Teichmüller disks in the Thurston boundary of Teichmüller space of a closed surface S of genus at least 2. It is well known that almost every Teichmüller geodesic ray converges to a point on the boundary. We show that unlike rays, Teichmüller disks with smallest possible limit sets are extremely rare.

Citations

• Teichmueller geodesics with d-dimensional limit sets
• Limit sets of Teichm "uller geodesics with minimal nonuniquely ergodic\n vertical foliation, II
• Finite translation surfaces with maximal number of translations
• Characterizations of lattice surfaces
• On the boundary of Teichmueller disks in Teichmueller and in Schottky space
• An extraordinary origami curve

Related

• Teichmueller geodesics with d-dimensional limit sets
• Divergent geodesics in the Universal Teichmüller space
• Limit sets of Weil-Petersson geodesics
• Visual sphere and Thurston's boundary of the Universal Teichm "uller\n space
• Limits in PMF of Teichmuller geodesics