Displaying similar documents to “On the existence of positive solutions of Yamabe-type equations on the Heisenberg group.”

Weyl submersions of Weyl manifolds

Fumio Narita (2007)

Colloquium Mathematicae

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We define Weyl submersions, for which we derive equations analogous to the Gauss and Codazzi equations for an isometric immersion. We obtain a necessary and sufficient condition for the total space of a Weyl submersion to admit an Einstein-Weyl structure. Moreover, we investigate the Einstein-Weyl structure of canonical variations of the total space with Einstein-Weyl structure.

Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem

Stefan Ivanov, Ivan Minchev, Dimiter Vassilev (2010)

Journal of the European Mathematical Society

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A complete solution to the quaternionic contact Yamabe problem on the seven-dimensional sphere is given. Extremals for the Sobolev inequality on the seven-dimensional Heisenberg group are explicitly described and the best constant in the L2 Folland–Stein embedding theorem is determined.

Weyl numbers versus Z-Weyl numbers

Bernd Carl, Andreas Defant, Doris Planer (2014)

Studia Mathematica

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Given an infinite-dimensional Banach space Z (substituting the Hilbert space ℓ₂), the s-number sequence of Z-Weyl numbers is generated by the approximation numbers according to the pattern of the classical Weyl numbers. We compare Weyl numbers with Z-Weyl numbers-a problem originally posed by A. Pietsch. We recover a result of Hinrichs and the first author showing that the Weyl numbers are in a sense minimal. This emphasizes the outstanding role of Weyl numbers within the theory of eigenvalue...

Relationships between generalized Heisenberg algebras and the classical Heisenberg algebra

Marc Fabbri, Frank Okoh (2014)

Colloquium Mathematicae

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A Lie algebra is called a generalized Heisenberg algebra of degree n if its centre coincides with its derived algebra and is n-dimensional. In this paper we define for each positive integer n a generalized Heisenberg algebra 𝓗ₙ. We show that 𝓗ₙ and 𝓗 ₁ⁿ, the Lie algebra which is the direct product of n copies of 𝓗 ₁, contain isomorphic copies of each other. We show that 𝓗ₙ is an indecomposable Lie algebra. We prove that 𝓗ₙ and 𝓗 ₁ⁿ are not quotients of each other when n ≥ 2, but...

Fourier-Wigner transforms and Liouville's theorems for the sub-Laplacian on the Heisenberg group

Aparajita Dasgupta, M. W. Wong (2010)

Banach Center Publications

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The sub-Laplacian on the Heisenberg group is first decomposed into twisted Laplacians parametrized by Planck's constant. Using Fourier-Wigner transforms so parametrized, we prove that the twisted Laplacians are globally hypoelliptic in the setting of tempered distributions. This result on global hypoellipticity is then used to obtain Liouville's theorems for harmonic functions for the sub-Laplacian on the Heisenberg group.

a-Weyl's theorem and perturbations

Mourad Oudghiri (2006)

Studia Mathematica

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We study the stability of a-Weyl's theorem under perturbations by operators in some known classes. We establish in particular that if T is a finite a-isoloid operator, then a-Weyl's theorem is transmitted from T to T + R for every Riesz operator R commuting with T.

Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation

Nicola Garofalo, Ermanno Lanconelli (1990)

Annales de l'institut Fourier

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A recent result of Bahouri shows that continuation from an open set fails in general for solutions of ℒ u = V u where V ∈ C ∞ and ℒ = ∑ j = 1 N - 1 X j 2 is a (nonelliptic) operator in R N satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when ℒ is the subelliptic Laplacian on the Heisenberg group and V is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of ℒ u = V u to have a...