Sharp Domains of Determinacy and Hamilton-Jacobi Equations

Jean-Luc Joly; Guy Métivier; Jeffrey Rauch

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Displaying similar documents to “Sharp Domains of Determinacy and Hamilton-Jacobi Equations”

Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting restricted normal Jacobi operators

Doo Hyun Hwang, Eunmi Pak, Changhwa Woo (2017)

Czechoslovak Mathematical Journal

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We give a classification of Hopf real hypersurfaces in complex hyperbolic two-plane Grassmannians ${SU}_{2, m} / S (U_{2} \cdot U_{m})$ with commuting conditions between the restricted normal Jacobi operator ${\bar{R}}_{N} φ$ and the shape operator $A$ (or the Ricci tensor $S$ ).

Generalized Tanaka-Webster and Levi-Civita connections for normal Jacobi operator in complex two-plane Grassmannians

Eunmi Pak, Juan de Dios Pérez, Young Jin Suh (2015)

Czechoslovak Mathematical Journal

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We study classifying problems of real hypersurfaces in a complex two-plane Grassmannian $G_{2} (ℂ^{m + 2})$ . In relation to the generalized Tanaka-Webster connection, we consider that the generalized Tanaka-Webster derivative of the normal Jacobi operator coincides with the covariant derivative. In this case, we prove complete classifications for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ satisfying such conditions.

Hamilton-Jacobi flows and characterization of solutions of Aronsson equations

Petri Juutinen, Eero Saksman (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In this note, we verify the conjecture of Barron, Evans and Jensen [3] regarding the characterization of viscosity solutions of general Aronsson equations in terms of the properties of associated forward and backwards Hamilton-Jacobi flows. A special case of this result is analogous to the characterization of infinity harmonic functions in terms of convexity and concavity of the functions $r \mapsto {max}_{y \in B_{r} (x)} u (y)$ and $r \mapsto {min}_{y \in B_{r} (x)} u (y)$ , respectively.

Hopf hypersurfaces in complex two-plane Grassmannians with generalized Tanaka-Webster parallel normal Jacobi operator

Eunmi Pak, Juan de Dios Pérez, Carlos J. G. Machado, Changhwa Woo (2015)

Czechoslovak Mathematical Journal

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We study the classifying problem of immersed submanifolds in Hermitian symmetric spaces. Typically in this paper, we deal with real hypersurfaces in a complex two-plane Grassmannian $G_{2} (ℂ^{m + 2})$ which has a remarkable geometric structure as a Hermitian symmetric space of rank 2. In relation to the generalized Tanaka-Webster connection, we consider a new concept of the parallel normal Jacobi operator for real hypersurfaces in $G_{2} (ℂ^{m + 2})$ and prove non-existence of real hypersurfaces in $G_{2} (ℂ^{m + 2})$ with generalized...

Sur la classification des hexagones hyperboliques à angles droits en dimension 5

François Delgove, Nicolas Retailleau (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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The aim of this paper is to give a classification of the right-angled hyperbolic hexagons in the real hyperbolic space $ℍ_{ℝ}^{5}$ , by using a quaternionic distance between geodesics in $ℍ_{ℝ}^{5}$ .

Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces

George Kyriazis, Pencho Petrushev, Yuan Xu (2008)

Studia Mathematica

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The Littlewood-Paley theory is extended to weighted spaces of distributions on [-1,1] with Jacobi weights $w (t) = {(1 - t)}^{α} {(1 + t)}^{β}$ . Almost exponentially localized polynomial elements (needlets) $φ_{ξ}$ , $ψ_{ξ}$ are constructed and, in complete analogy with the classical case on ℝⁿ, it is shown that weighted Triebel-Lizorkin and Besov spaces can be characterized by the size of the needlet coefficients $⟨ f, φ_{ξ} ⟩$ in respective sequence spaces.

$C^{\infty}$ -well posedness of the Cauchy problem for quasi-linear hyperbolic equations with coefficients non-Lipschitz in time and smooth in space

Akisato Kubo, Michael Reissig (2003)

Banach Center Publications

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In this paper we prove the $C^{\infty}$ -well posedness of the Cauchy problem for quasi-linear hyperbolic equations of second order with coefficients non-Lipschitz in t ∈ [0,T] and smooth in x ∈ ℝⁿ.

Hyperbolic spaces in Teichmüller spaces

Christopher J. Leininger, Saul Schleimer (2014)

Journal of the European Mathematical Society

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We prove, for any $n$ , that there is a closed connected orientable surface $S$ so that the hyperbolic space $ℍ^{n}$ almost-isometrically embeds into the Teichmüller space of $S$ , with quasi-convex image lying in the thick part. As a consequence, $ℍ^{n}$ quasi-isometrically embeds in the curve complex of $S$ .

A generalization of Bateman's expansion and finite integrals of Sonine's and Feldheim's type

Giacomo Gigante (2010)

Colloquium Mathematicae

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Let ${A_{k}}_{k = 0}^{+ \infty}$ be a sequence of arbitrary complex numbers, let α,β > -1, let Pₙα,βn=0+∞ $b e t h e J a c o b i p o l y n o m i a l s a n d d e f i n e t h e f u n c t i o n s$ $H ₙ (α, z) = \sum_{m = n}^{+ \infty} (A_{m} z^{m}) / (Γ (α + n + m + 1) (m - n)!)$ , $G (α, β, x, y) = \sum_{r, s = 0}^{+ \infty} (A_{r + s} x^{r} y^{s}) / (Γ (α + r + 1) Γ (β + s + 1) r! s!)$ . Then, for any non-negative integer n, $\int_{0}^{π / 2} G (α, β, x ² s i n ² ϕ, y ² c o s ² ϕ) P ₙ^{α, β} (c o s ² ϕ) s i n^{2 α + 1} ϕ c o s^{2 β + 1} ϕ d = 1 / 2 H ₙ (α + β + 1, x ² + y ²) P ₙ^{α, β} ((y ² - x ²) / (y ² + x ²))$ . When $A_{k} = {(- 1 / 4)}^{k}$ , this formula reduces to Bateman’s expansion for Bessel functions. For particular values of y and n one obtains generalizations of several formulas already known for Bessel functions, like Sonine’s first and second finite integrals and certain Neumann series expansions. Particular choices of ${A_{k}}_{k = 0}^{+ \infty}$ allow one to write all these type of formulas...