L¹-convergence and hypercontractivity of diffusion semigroups on manifolds

Feng-Yu Wang

Displaying similar documents to “L¹-convergence and hypercontractivity of diffusion semigroups on manifolds”

On some properties of a Riemannian space $V_{4}$ with constant scalar curvature

W. Slósarska, Z. Żekanowski (1972)

Colloquium Mathematicae

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Riemannian semisymmetric almost Kenmotsu manifolds and nullity distributions

Yaning Wang, Ximin Liu (2014)

Annales Polonici Mathematici

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We consider an almost Kenmotsu manifold $M^{2 n + 1}$ with the characteristic vector field ξ belonging to the (k,μ)’-nullity distribution and h’ ≠ 0 and we prove that $M^{2 n + 1}$ is locally isometric to the Riemannian product of an (n+1)-dimensional manifold of constant sectional curvature -4 and a flat n-dimensional manifold, provided that $M^{2 n + 1}$ is ξ-Riemannian-semisymmetric. Moreover, if $M^{2 n + 1}$ is a ξ-Riemannian-semisymmetric almost Kenmotsu manifold such that ξ belongs to the (k,μ)-nullity distribution, we prove...

On $2p$ -dimensional Riemannian manifolds with positive scalar curvature

Domenico Perrone (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In questo lavoro si danno alcuni risultati sugli spettri degli operatori di Laplace per varietà Riemanniane compatte con curvatura scalare positiva e di dimensione $2p$ . Ad essi si aggiunge una osservazione riguardante la congettura di Yamabe.

Collapse of warped submersions

Szymon M. Walczak (2006)

Annales Polonici Mathematici

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We generalize the concept of warped manifold to Riemannian submersions π: M → B between two compact Riemannian manifolds $(M, g_{M})$ and $(B, g_{B})$ in the following way. If f: B → (0,∞) is a smooth function on B which is extended to a function f̂ = f ∘ π constant along the fibres of π then we define a new metric $g_{f}$ on M by $g_{f} |_{\times} \equiv g_{M} |_{\times}, g_{f} {|_{\times T M ̂} \equiv f ̂ ² g_{M} |}_{\times T M ̂}$ , where and denote the bundles of horizontal and vertical vectors. The manifold $(M, g_{f})$ obtained that way is called a warped submersion. The function f is called a warping function. We show...

Semigroups generated by convex combinations of several Feller generators in models of mathematical biology

Adam Bobrowski, Radosław Bogucki (2008)

Studia Mathematica

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Let be a locally compact Hausdorff space. Let $A_{i}$ , i = 0,1,...,N, be generators of Feller semigroups in C₀() with related Feller processes $X_{i} = X_{i} (t), t \geq 0$ and let $α_{i}$ , i = 0,...,N, be non-negative continuous functions on with $\sum_{i = 0}^{N} α_{i} = 1$ . Assume that the closure A of $\sum_{k = 0}^{N} α_{k} A_{k}$ defined on $⋂_{i = 0}^{N} (A_{i})$ generates a Feller semigroup T(t), t ≥ 0 in C₀(). A natural interpretation of a related Feller process X = X(t), t ≥ 0 is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ , with probability...

Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds

Nguyen Ngoc Khanh (2016)

Archivum Mathematicum

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In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds $(M, g)$ for the following general heat equation $u_{t} = Δ_{V} u + a u log u + b u$ where $a$ is a constant and $b$ is a differentiable function defined on $M \times [0, \infty)$ . We suppose that the Bakry-Émery curvature and the $N$ -dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y. Li ([6]), recently. ...

Structure of second-order symmetric Lorentzian manifolds

Oihane F. Blanco, Miguel Sánchez, José M. Senovilla (2013)

Journal of the European Mathematical Society

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$𝑆𝑒𝑐𝑜𝑛𝑑 - 𝑜𝑟𝑑𝑒𝑟𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑖𝑐𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛𝑠𝑝𝑎𝑐𝑒𝑠$ , that is to say, Lorentzian manifolds with vanishing second derivative $\nabla \nabla R \equiv 0$ of the curvature tensor $R$ , are characterized by several geometric properties, and explicitly presented. Locally, they are a product $M = M_{1} \times M_{2}$ where each factor is uniquely determined as follows: $M_{2}$ is a Riemannian symmetric space and $M_{1}$ is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., $\nabla R \neq 0$ at some point), the curvature...

Pointwise convergence of nonconventional averages

I. Assani (2005)

Colloquium Mathematicae

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We answer a question of H. Furstenberg on the pointwise convergence of the averages $1 / N \sum_{n = 1}^{N} U ⁿ (f \cdot R ⁿ (g))$ , where U and R are positive operators. We also study the pointwise convergence of the averages $1 / N \sum_{n = 1}^{N} f (S ⁿ x) g (R ⁿ x)$ when T and S are measure preserving transformations.

On $2p$ -dimensional Riemannian manifolds with positive scalar curvature

Domenico Perrone (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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On $G$ -sets and isospectrality

Ori Parzanchevski (2013)

Annales de l’institut Fourier

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We study finite $G$ -sets and their tensor product with Riemannian manifolds, and obtain results on isospectral quotients and covers. In particular, we show the following: If $M$ is a compact connected Riemannian manifold (or orbifold) whose fundamental group has a finite non-cyclic quotient, then $M$ has isospectral non-isometric covers.

Local gradient estimates of $p$ -harmonic functions, $1 / H$ -flow, and an entropy formula

Brett Kotschwar, Lei Ni (2009)

Annales scientifiques de l'École Normale Supérieure

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In the first part of this paper, we prove local interior and boundary gradient estimates for $p$ -harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an existence theorem for weak solutions to the level set formulation of the $1 / H$ (inverse mean curvature) flow for hypersurfaces in ambient manifolds satisfying a sharp volume growth assumption. In the second part of this paper, we consider two parabolic analogues...

On Uniqueness Theoremsfor Ricci Tensor

Marina B. Khripunova, Sergey E. Stepanov, Irina I. Tsyganok, Josef Mikeš (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$ , construct a metric on $M$ whose Ricci tensor equals $r$ . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with...

Convergence in the dual of certain $K M_{p}$ -spaces

Larry Kitchens, Charles Swartz (1974)

Colloquium Mathematicae

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Tenseness of Riemannian flows

Hiraku Nozawa, José Ignacio Royo Prieto (2014)

Annales de l’institut Fourier

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We show that any transversally complete Riemannian foliation $ℱ$ of dimension one on any possibly non-compact manifold $M$ is tense; namely, $M$ admits a Riemannian metric such that the mean curvature form of $ℱ$ is basic. This is a partial generalization of a result of Domínguez, which says that any Riemannian foliation on any compact manifold is tense. Our proof is based on some results of Molino and Sergiescu, and it is simpler than the original proof by Domínguez. As an application, we generalize...

Inverses of generators of nonanalytic semigroups

Ralph deLaubenfels (2009)

Studia Mathematica

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Suppose A is an injective linear operator on a Banach space that generates a uniformly bounded strongly continuous semigroup ${e^{t A}}_{t \geq 0}$ . It is shown that $A^{- 1}$ generates an $O (1 + τ) A {(1 - A)}^{- 1}$ -regularized semigroup. Several equivalences for $A^{- 1}$ generating a strongly continuous semigroup are given. These are used to generate sufficient conditions on the growth of ${e^{t A}}_{t \geq 0}$ , on subspaces, for $A^{- 1}$ generating a strongly continuous semigroup, and to show that the inverse of -d/dx on the closure of its image in L¹([0,∞)) does not generate...

On the completeness of $ℒ_{p}$ -spaces over a charge

Sreela Gangopadhyay (1990)

Colloquium Mathematicae

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On semigroups of $σ$ -endomorphisms

Iwanik, Anzelm

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On smoothing properties of transition semigroups associated to a class of SDEs with jumps

Seiichiro Kusuoka, Carlo Marinelli (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We prove smoothing properties of nonlocal transition semigroups associated to a class of stochastic differential equations (SDE) in $ℝ^{d}$ driven by additive pure-jump Lévy noise. In particular, we assume that the Lévy process driving the SDE is the sum of a subordinated Wiener process $Y$ (i.e. $Y = W \circ T$ , where $T$ is an increasing pure-jump Lévy process starting at zero and independent of the Wiener process $W$ ) and of an arbitrary Lévy process independent of $Y$ , that the drift coefficient is continuous...

Nilakantha's accelerated series for π

David Brink (2015)

Acta Arithmetica

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We show how the idea behind a formula for π discovered by the Indian mathematician and astronomer Nilakantha (1445-1545) can be developed into a general series acceleration technique which, when applied to the Gregory-Leibniz series, gives the formula $π = \sum_{n = 0}^{\infty} ((5 n + 3) n! (2 n)!) / (2^{n - 1} (3 n + 2)!)$ with convergence as $13 . 5^{- n}$ , in much the same way as the Euler transformation gives $π = \sum_{n = 0}^{\infty} (2^{n + 1} n! n!) / (2 n + 1)!$ with convergence as $2^{- n}$ . Similar transformations lead to other accelerated series for π, including three “BBP-like” formulas, all of which are collected in...

On ultra-weak convergence in $L^{p}$

Donald E. Myers (1976)

Annales Polonici Mathematici

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