On the group of real analytic diffeomorphisms

Takashi Tsuboi

Displaying similar documents to “On the group of real analytic diffeomorphisms”

Radii of p-valence of certain analytic functions of order $α$ with negative coefficients

M. K. Aouf (1989)

Matematički Vesnik

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Finite actions on the Klein four-orbifold and prism manifolds

John Kalliongis, Ryo Ohashi (2017)

Commentationes Mathematicae Universitatis Carolinae

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We describe the finite group actions, up to equivalence, which can act on the orbifold $Σ (2, 2, 2)$ , and their quotient types. This is then used to consider actions on prism manifolds $M (b, d)$ which preserve a longitudinal fibering, but do not leave any Heegaard Klein bottle invariant. If $ϕ : G \to Homeo (M (b, d))$ is such an action, we show that $M (b, d) = M (b, 2)$ and $M (b, 2) / ϕ$ fibers over a certain collection of 2-orbifolds with positive Euler characteristic which are covered by $Σ (2, 2, 2)$ . For the standard actions, we compute the fundamental group of $M (b, 2) / ϕ$ and...

Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^{n}$

J. Siciak (1969)

Annales Polonici Mathematici

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$Z ₂^{k}$ -actions with a special fixed point set

Pedro L. Q. Pergher, Rogério de Oliveira (2005)

Fundamenta Mathematicae

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Let Fⁿ be a connected, smooth and closed n-dimensional manifold satisfying the following property: if $N^{m}$ is any smooth and closed m-dimensional manifold with m > n and $T : N^{m} \to N^{m}$ is a smooth involution whose fixed point set is Fⁿ, then m = 2n. We describe the equivariant cobordism classification of smooth actions $(M^{m}; Φ)$ of the group $G = Z ₂^{k}$ on closed smooth m-dimensional manifolds $M^{m}$ for which the fixed point set of the action is a submanifold Fⁿ with the above property. This generalizes a result of F....

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

Jagannath Patel, Ashok Kumar Sahoo (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class $R^{λ} (a, c, A, B)$ of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass ${\tilde{R}}^{λ} (a, c, A, B)$ of $R^{λ} (a, c, A, B)$ and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.

Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds

Laurent Meersseman (2011)

Annales scientifiques de l'École Normale Supérieure

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Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of $0$ in $ℂ^{p}$ , for some $p > 0$ ) or differentiable (parametrized by an open neighborhood of $0$ in $ℝ^{p}$ , for some $p > 0$ ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point $t$ of the parameter space, the fiber over $t$ of the first family is biholomorphic to the fiber over $t$ of the second family. Then, under which conditions...

Divisors in global analytic sets

Francesca Acquistapace, A. Díaz-Cano (2011)

Journal of the European Mathematical Society

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We prove that any divisor $Y$ of a global analytic set $X \subset ℝ^{n}$ has a generic equation, that is, there is an analytic function vanishing on $Y$ with multiplicity one along each irreducible component of $Y$ . We also prove that there are functions with arbitrary multiplicities along $Y$ . The main result states that if $X$ is pure dimensional, $Y$ is locally principal, $X / Y$ is not connected and $Y$ represents the zero class in $H_{q - 1}^{\infty} (X, ℤ_{2})$ then the divisor $Y$ is globally principal.

On the rigidity of webs

Michel Belliart (2007)

Bulletin de la Société Mathématique de France

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Plane $d$ -webs have been studied a lot since their appearance at the turn of the 20th century. A rather recent and striking result for them is the theorem of Dufour, stating that the measurable conjugacies between 3-webs have to be analytic. Here, we show that even the set-theoretic conjugacies between two $d$ -webs, $d \geq 3$ are analytic unless both webs are analytically parallelizable. Between two set-theoretically conjugate parallelizable $d$ -webs, however, there always exists a nonmeasurable conjugacy;...

Properties of functions concerned with Caratheodory functions

Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let $𝒫_{n}$ denote the class of analytic functions $p (z)$ of the form $p (z) = 1 + c_{n} z^{n} + c_{n + 1} z^{n + 1} + \dots$ in the open unit disc $𝕌$ . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for $p (z)$ concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.

Non-orbit equivalent actions of $𝔽_{n}$

Adrian Ioana (2009)

Annales scientifiques de l'École Normale Supérieure

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For any $2 \leq n \leq \infty$ , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group $𝔽_{n}$ . These actions arise as diagonal products between a generalized Bernoulli action and the action $𝔽_{n} ↷ (𝕋^{2}, λ^{2})$ , where $𝔽_{n}$ is seen as a subgroup of ${SL}_{2} (ℤ)$ .

Maximum modulus in a bidisc of analytic functions of bounded $𝐋$ -index and an analogue of Hayman’s theorem

Andriy Bandura, Nataliia Petrechko, Oleh Skaskiv (2018)

Mathematica Bohemica

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We generalize some criteria of boundedness of $𝐋$ -index in joint variables for in a bidisc analytic functions. Our propositions give an estimate the maximum modulus on a skeleton in a bidisc and an estimate of $(p + 1)$ th partial derivative by lower order partial derivatives (analogue of Hayman’s theorem).

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: $1_{}$ . if M is a linear manifold, then (M) contains convex functions, $2_{}$ . (·) is invariant under diffeomorphisms, $3_{}$ . each f ∈ (M) is differentiable on a dense $G_{δ}$ -set, is investigated.

Persistence of fixed points under rigid perturbations of maps

Salvador Addas-Zanata, Pedro A. S. Salomão (2014)

Fundamenta Mathematicae

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Let f: S¹ × [0,1] → S¹ × [0,1] be a real-analytic diffeomorphism which is homotopic to the identity map and preserves an area form. Assume that for some lift f̃: ℝ × [0,1] → ℝ × [0,1] we have Fix(f̃) = ℝ × 0 and that f̃ positively translates points in ℝ × 1. Let $f ̃_{ϵ}$ be the perturbation of f̃ by the rigid horizontal translation (x,y) ↦ (x+ϵ,y). We show that $F i x (f ̃_{ϵ}) = \emptyset$ for all ϵ > 0 sufficiently small. The proof follows from Kerékjártó’s construction of Brouwer lines for orientation preserving...

Shadowing in actions of some Abelian groups

Sergei Yu. Pilyugin, Sergei B. Tikhomirov (2003)

Fundamenta Mathematicae

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We study shadowing properties of continuous actions of the groups $ℤ^{p}$ and $ℤ^{p} \times ℝ^{p}$ . Necessary and sufficient conditions are given under which a linear action of $ℤ^{p}$ on $ℂ^{m}$ has a Lipschitz shadowing property.

Explicit computations of all finite index bimodules for a family of II $_{1}$ factors

Stefaan Vaes (2008)

Annales scientifiques de l'École Normale Supérieure

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We study II $_{1}$ factors $M$ and $N$ associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index $M$ - $N$ -bimodule (in particular, every isomorphism between $M$ and $N$ ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index $M$ - $M$ -bimodules is identified with an extended Hecke fusion algebra,...

On Hattori spaces

A. Bouziad, E. Sukhacheva (2017)

Commentationes Mathematicae Universitatis Carolinae

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For a subset $A$ of the real line $ℝ$ , Hattori space $H (A)$ is a topological space whose underlying point set is the reals $ℝ$ and whose topology is defined as follows: points from $A$ are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on $A$ which are sufficient and necessary for $H (A)$ to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated...

A pure smoothness condition for Radó’s theorem for $α$ -analytic functions

Abtin Daghighi, Frank Wikström (2016)

Czechoslovak Mathematical Journal

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Let $Ω \subset ℂ^{n}$ be a bounded, simply connected $ℂ$ -convex domain. Let $α \in ℤ_{+}^{n}$ and let $f$ be a function on $Ω$ which is separately $C^{2 α_{j} - 1}$ -smooth with respect to $z_{j}$ (by which we mean jointly $C^{2 α_{j} - 1}$ -smooth with respect to $Re z_{j}$ , $Im z_{j}$ ). If $f$ is $α$ -analytic on $Ω ∖ f^{- 1} (0)$ , then $f$ is $α$ -analytic on $Ω$ . The result is well-known for the case $α_{i} = 1$ , $1 \leq i \leq n$ , even when $f$ a priori is only known to be continuous.