The Schottky Problem on Pants
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY(1988)
Abstract
In this note, we consider the classical problem of Schottky of characterizing the set of period matrices which arise from all possible conformal structures on a fixed topological surface. Restricting to a planar surface with Euler characteristic − 1 - 1 , we find that a real symmetric 3 3 -by- 3 3 matrix arises as a period matrix if and only if the matrix has vanishing row sums, and the diagonal entries are positive and satisfy all three possible strict triangle inequalities. The technique of proof involves extremal and harmonic lengths of curve classes.
MoreTranslated text
Key words
schottky problem
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined