scholarly journals The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

2007 ◽  
Vol 30 (1) ◽  
pp. 17-49 ◽  
Author(s):  
Vittorio Barone Adesi ◽  
Francesco Serra Cassano ◽  
Davide Vittone
Keyword(s):  
Heisenberg Groups ◽  
Bernstein Problem

scholarly journals Counting and equidistribution in quaternionic Heisenberg groups

2021 ◽  
pp. 1-38
Author(s):  
JOUNI PARKKONEN ◽  
FRÉDÉRIC PAULIN
Keyword(s):  
Hyperbolic Geometry ◽  
Quaternion Algebra ◽  
Rational Points ◽  
Hyperbolic Spaces ◽  
Heisenberg Groups ◽  
Arithmetic Groups ◽  
Hermitian Forms ◽  
Dimension 2 ◽  
Counting Formula ◽  
The Relationship

Abstract We develop the relationship between quaternionic hyperbolic geometry and arithmetic counting or equidistribution applications, that arises from the action of arithmetic groups on quaternionic hyperbolic spaces, especially in dimension 2. We prove a Mertens counting formula for the rational points over a definite quaternion algebra A over ${\mathbb{Q}}$ in the light cone of quaternionic Hermitian forms, as well as a Neville equidistribution theorem of the set of rational points over A in quaternionic Heisenberg groups.

scholarly journals Quantum Heisenberg groups and sklyanin algebras

1994 ◽  
Vol 31 (3) ◽  
pp. 167-177 ◽  
Author(s):  
Nicol�s Andruskiewitsch ◽  
Jorge Devoto ◽  
Alejandro Tiraboschi
Keyword(s):  
Heisenberg Groups ◽  
Sklyanin Algebras

scholarly journals The Bernstein Problem in Dimension 6

1996 ◽  
Vol 185 (2) ◽  
pp. 420-439 ◽  
Author(s):  
J.Carlos Gutierrez Fernandez
Keyword(s):  
Bernstein Problem

scholarly journals Finite Heisenberg groups in quiver gauge theories

2006 ◽  
Vol 747 (3) ◽  
pp. 436-454 ◽  
Author(s):  
Benjamin A. Burrington ◽  
James T. Liu ◽  
Leopoldo A. Pando Zayas
Keyword(s):  
Gauge Theories ◽  
Heisenberg Groups

scholarly journals Solution of the Bernstein Problem in the Non-regular Case

2000 ◽  
Vol 223 (1) ◽  
pp. 109-132 ◽  
Author(s):  
J.Carlos Gutiérrez Fernández
Keyword(s):  
Regular Case ◽  
Bernstein Problem

Fundamental Solutions of Kohn Sub-Laplacians on Anisotropic Heisenberg Groups and H-type Groups

2011 ◽  
Vol 54 (1) ◽  
pp. 126-140 ◽  
Author(s):  
Yongyang Jin ◽  
Genkai Zhang
Keyword(s):  
Fundamental Solutions ◽  
Meromorphic Continuation ◽  
Heisenberg Groups ◽  
Tempered Distributions

AbstractWe prove that the fundamental solutions of Kohn sub-LaplaciansΔ+iα∂t on the anisotropic Heisenberg groups are tempered distributions and have meromorphic continuation in α with simple poles. We compute the residues and find the partial fundamental solutions at the poles. We also find formulas for the fundamental solutions for some matrix-valued Kohn type sub-Laplacians on H-type groups.

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