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Hull-minimal ideals in the Schwartz algebra of the Heisenberg group

J. Ludwig (1998)

Studia Mathematica

For every closed subset C in the dual space $Ĥ_{n}$ of the Heisenberg group $H_{n}$ we describe via the Fourier transform the elements of the hull-minimal ideal j(C) of the Schwartz algebra $S (H_{n})$ and we show that in general for two closed subsets $C_{1}, C_{2}$ of $Ĥ_{n}$ the product of $j (C_{1})$ and $j (C_{2})$ is different from $j (C_{1} \cap C_{2})$ .

Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces

Francesca Astengo, Bianca Di Blasio (2010)

Annales mathématiques Blaise Pascal

We prove that Huygens’ principle and the principle of equipartition of energy hold for the modified wave equation on odd dimensional Damek–Ricci spaces. We also prove a Paley–Wiener type theorem for the inverse of the Helgason Fourier transform on Damek–Ricci spaces.

Hyperbolic 4-manifolds and conformally flat 3-manifolds

Michael Gromov, H. B. Jr. Lawson, W. Thurston (1988)

Publications Mathématiques de l'IHÉS

Hyperbolic 4-manifolds and tesselations

Nicholaas H. Kuiper (1988)

Publications Mathématiques de l'IHÉS

Hyperbolic geometry and moduli of real cubic surfaces

Daniel Allcock, James A. Carlson, Domingo Toledo (2010)

Annales scientifiques de l'École Normale Supérieure

Let $ℳ_{0}^{ℝ}$ be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space $H^{4}$ and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in $PO (4, 1)$ . We also derive several new and several old results on the topology of $ℳ_{0}^{ℝ}$ ....