A Generalization of the Isoperimetric Inequality on S 2 and Flat Tori in S 3

1994 ◽  
Vol 120 (2) ◽  
pp. 553
Author(s):  
Kazuyuki Enomoto
Keyword(s):  
Isoperimetric Inequality ◽  
Flat Tori

scholarly journals An isoperimetric inequality for an integral operator on flat tori

2015 ◽  
Vol 59 (3) ◽  
pp. 773-793
Author(s):  
Braxton Osting ◽  
Jeremy Marzuola ◽  
Elena Cherkaev
Keyword(s):  
Integral Operator ◽  
Isoperimetric Inequality ◽  
Flat Tori

scholarly journals A note on moduli spaces of conformal classes for flat tori of higher dimension and on their conformal multiplication

2021 ◽  
Author(s):  
Anna Gori ◽  
Alberto Verjovsky ◽  
Fabio Vlacci
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Abelian Varieties ◽  
Complex Multiplication ◽  
Higher Dimension ◽  
Geometric Constructions ◽  
Flat Torus ◽  
Flat Tori

AbstractMotivated by the theory of complex multiplication of abelian varieties, in this paper we study the conformality classes of flat tori in $${\mathbb {R}}^{n}$$ R n and investigate criteria to determine whether a n-dimensional flat torus has non trivial (i.e. bigger than $${\mathbb {Z}}^{*}={\mathbb {Z}}{\setminus }\{0\}$$ Z ∗ = Z \ { 0 } ) semigroup of conformal endomorphisms (the analogs of isogenies for abelian varieties). We then exhibit several geometric constructions of tori with this property and study the class of conformally equivalent lattices in order to describe the moduli space of the corresponding tori.

Minima of Epstein’s Zeta function and heights of flat tori

2006 ◽  
Vol 165 (1) ◽  
pp. 115-151 ◽  
Author(s):  
Peter Sarnak ◽  
Andreas Strömbergsson
Keyword(s):  
Zeta Function ◽  
Flat Tori

An isoperimetric inequality for the principal eigenvalue of the Laplacian with drift

2005 ◽  
Vol 340 (5) ◽  
pp. 347-352 ◽  
Author(s):  
François Hamel ◽  
Nikolai Nadirashvili ◽  
Emmanuel Russ
Keyword(s):  
Isoperimetric Inequality ◽  
Principal Eigenvalue

scholarly journals Moduli Spaces of Flat Tori with Prescribed Holonomy

2017 ◽  
Vol 27 (6) ◽  
pp. 1289-1366
Author(s):  
Selim Ghazouani ◽  
Luc Pirio
Keyword(s):  
Moduli Spaces ◽  
Flat Tori
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