TY - JOUR
T1 - Translation surfaces with no convex presentation
AU - Lelièvre, Samuel
AU - Weiss, Barak
N1 - Publisher Copyright:
© 2015, Springer International Publishing.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - We give infinite lists of translation surfaces with no convex presentations. We classify the surfaces in the stratum H(2) which do not have convex presentations, as well as those with no strictly convex presentations. We show that in H(1,1), all surfaces in the eigenform loci (Formula presented.) or ε16 have no strictly convex presentation, and that the list of surfaces with no convex presentations in (Formula presented.) is finite and consists of square-tiled surfaces. We prove the existence of non-lattice surfaces without strictly convex presentations in all of the strata (Formula presented.).
AB - We give infinite lists of translation surfaces with no convex presentations. We classify the surfaces in the stratum H(2) which do not have convex presentations, as well as those with no strictly convex presentations. We show that in H(1,1), all surfaces in the eigenform loci (Formula presented.) or ε16 have no strictly convex presentation, and that the list of surfaces with no convex presentations in (Formula presented.) is finite and consists of square-tiled surfaces. We prove the existence of non-lattice surfaces without strictly convex presentations in all of the strata (Formula presented.).
UR - http://www.scopus.com/inward/record.url?scp=84949094711&partnerID=8YFLogxK
U2 - 10.1007/s00039-015-0349-0
DO - 10.1007/s00039-015-0349-0
M3 - Article
AN - SCOPUS:84949094711
SN - 1016-443X
VL - 25
SP - 1902
EP - 1936
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 6
ER -