scholarly journals Random Moments for the New Eigenfunctions of Point Scatterers on Rectangular Flat Tori

2021 ◽  
Author(s):  
Thomas Letendre ◽  
Henrik Ueberschär
Keyword(s):  
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

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

scholarly journals Quantum chaos for point scatterers on flat tori

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120509 ◽  
Author(s):  
Henrik Ueberschär
Keyword(s):  
Wave Function ◽  
Strong Coupling ◽  
Quantum Chaos ◽  
Recent Progress ◽  
Three Dimensional ◽  
Point Scatterer ◽  
Open Problems ◽  
Survey Article ◽  
Delta Potential ◽  
Flat Tori

This survey article deals with a delta potential—also known as a point scatterer—on flat two- and three-dimensional tori. We introduce the main conjectures regarding the spectral and wave function statistics of this model in the so-called weak and strong coupling regimes. We report on recent progress as well as a number of open problems in this field.

scholarly journals Embedded flat tori in the unit $3$ -sphere

1995 ◽  
Vol 47 (2) ◽  
pp. 275-296 ◽  
Author(s):  
Yoshihisa KITAGAWA
Keyword(s):  
Flat Tori

scholarly journals Spectral asymptotics of all the eigenvalues of Schrödinger operators on flat tori

2022 ◽  
Vol 216 ◽  
pp. 112679
Author(s):  
Dario Bambusi ◽  
Beatrice Langella ◽  
Riccardo Montalto
Keyword(s):  
Schrödinger Operators ◽  
Spectral Asymptotics ◽  
Schrodinger Operators ◽  
Flat Tori

scholarly journals Transverse J-holomorphic curves in nearly Kähler $$\mathbb {CP}^3$$

2021 ◽  
Author(s):  
Benjamin Aslan
Keyword(s):  
Minimal Surfaces ◽  
Type Theorem ◽  
Holomorphic Curves ◽  
Nearly Kähler ◽  
Flat Tori

AbstractJ-holomorphic curves in nearly Kähler $$\mathbb {CP}^3$$ CP 3 are related to minimal surfaces in $$S^4$$ S 4 as well as associative submanifolds in $$\Lambda ^2_-(S^4)$$ Λ - 2 ( S 4 ) . We introduce the class of transverse J-holomorphic curves and establish a Bonnet-type theorem for them. We classify flat tori in $$S^4$$ S 4 and construct moment-type maps from $$\mathbb {CP}^3$$ CP 3 to relate them to the theory of $$\mathrm {U}(1)$$ U ( 1 ) -invariant minimal surfaces on $$S^4$$ S 4 .

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
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