Paper finds surfaces where KVol is close to the surface's genus.
problem Finding the minimum KVol on translation surfaces.
method Constructing families of translation surfaces in .
result KVol can be made arbitrarily close to the surface's genus.
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5 results for “KVol”
Estimates KVol on surfaces with geometric constraints.
problem Determining the intersection of closed curves on translation surfaces.
method Geometric constraints on angles and indentifications of sides.
result Sharp estimate for KVol on Bouw-Möller surfaces with a unique singularity.
Bounds on intersection number for right-angled triangles.
problem Estimating intersection numbers in Teichmüller spaces.
method Analyzing moduli spaces of translation surfaces and Teichmüller discs.
result Sharp bounds on KVol function for specific Teichmüller discs.
Study intersections of curves on translation surfaces, focusing on regular polygons and their Teichmüller disks.
problem Maximizing algebraic intersection between curves of given lengths.
method Investigate the quantity KVol defined for any closed orientable surface, focusing on regular n-gons for even n ≥ 8.
result Maximize algebraic intersection between curves of given lengths.
This paper calculates interaction strength for translation surfaces with multiple singularities.
problem Computing the interaction strength of translation surfaces with multiple singularities is challenging.
method The authors study interaction strength of specific families of translation surfaces, including regular polygons and Bouw-Möller surfaces.
result The paper provides exact computations of KVol on translation surfaces with multiple singularities.