Related papers: On the Gromov non-embedding theorem
The analog of the Kepler system defined on the Heisenberg group introduced by Montgomery and Shanbrom in [Fields Inst. Commun., Vol. 73, Springer, New York, 2015, 319-342, arXiv:1212.2713] is integrable on the zero level of the Hamiltonian.…
We show that the fundamental group is not invariant under derived equivalence of smooth projective varieties.
In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the…
In \cite{BAMU}, an ergodic theorem \`a la Birkhoff-von Neumann for the action of the fundamental group of a compact negatively curved manifold on the boundary of its universal cover is proved. A quick corollary is the irreducibility of the…
We suggest a modified and briefer version for the proof of Higman's embedding theorem stating that a finitely generated group can be embedded in a finitely presented group if and only if it is recursively presented. In particular, we…
We show that the sharp constant in the Hardy-Littlewood-Sobolev inequality can be derived using the method that we employed earlier for a similar inequality on the Heisenberg group. The merit of this proof is that it does not rely on…
We generalize the graphical small cancellation theory of Gromov to a graphical small cancellation theory over the free product. We extend Gromov's small cancellation theorem to the free product. We explain and generalize Rips-Segev's…
In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.
We study the uniformization conjecture of Yau by using the Gromov-Haudorff convergence. As a consequence, we confirm Yau's finite generation conjecture. More precisely, on a complete noncompact K\"ahler manifold with nonnegative bisectional…
An embedding construction $G\hookrightarrow H$ for groups $G$ with a length function was introduced by the author earlier. Here we obtain new properties of this embedding, answering some questions raised by M.V. Sapir. In particular, an…
We extend Gromov's notion of asymptotic dimension of finitely generated groups to all discrete groups. In particular, we extend the Hurewicz type theorem proven in [B-D2] to general groups. Then we use this extension to prove a formula for…
We prove maximal ergodic theorems for spherical averages on the Heisenberg groups acting on $L_p$ spaces over measure spaces not necessarily commutative, that is, on noncommutative $L_p$ spaces. The scale of $p$ is optimal in the reduced…
We formulate and prove an analogue of Beurling's theorem for the Fourier transform on the Heisenberg group. As a consequence we deduce Hardy and Cowling-Price theorems.
We determine the all-genus Hodge-Gromov-Witten theory of a smooth hypersurface in weighted projective space defined by a chain or loop polynomial. In particular, we obtain the first genus-zero computation of Gromov-Witten invariants for…
We provide an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. We also prove that all Gromov-Witten classes of all smooth complete…
We establish the following theorem of Bernstein type for the first Heisenberg group: Let S be a C^2 connected H-minimal surface which is a graph over some plane P, then S is either a non-characteristic vertical plane, or its generalized…
We construct a new family of irreducible unitary representations of a finitely generated virtually free group L. We prove furthermore a general result concerning representations of Gromov hyperbolic groups that are weakly contained in the…
We present a new result on the nonexistence of generalized bent functions (GBFs)from (Z/tZ)^n to Z/tZ (called type [n, t]) for a large class. Assume p is an odd prime number. By showing certain quadratic norm form equations having no…
Continuing our previous work (Cohn, Lam, Lu, Yang, Nonlinear Analysis (2011), doi: 10.1016 /j.na.2011.09.053), we obtain a class of Trudinger-Moser inequalities on the entire Heisenberg group, which indicate what the best constants are. All…
We extend Ribet's Nondegeneracy theorem to all odd weight Hodge structures.