Geometric Separation in $$mathbb {R}^3$$ R 3

Journal of Fourier Analysis and Applications - The geometric separation problem, initially posed by Donoho and Kutyniok (Commun Pure Appl Math 66:1–47, 2013), aims to separate a distribution...     

On Some Spectral Properties of Pseudo-differential Operators on $$mathbb {T}$$ T

Journal of Fourier Analysis and Applications - In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential...     

Foliations on $$mathbb {P}^2$$ P 2 with only one singular point

Geometriae Dedicata - We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of...     

A short note on a class of Weingarten hypersurfaces in $$mathbb {R}^{n + 1}$$ R n + 1

Geometriae Dedicata - We provide sharp bounds for the squared norm of the second fundamental form of a wide class of Weingarten hypersurfaces in Euclidean space satisfying $$H_r = aH + b$$ , for...     

Set-theoretic complete intersection monomial curves in $${\mathbb{P}^n}$$

In this paper, we give a sufficient numerical criterion for a monomial curve in a projective space to be a set-theoretic complete intersection. Our main result generalizes a similar statement proven by Keum for monomial curves in three-dimensional projective space. We also prove that there are infinitely many set-theoretic complete intersection monomial curves in the projective n?space for any suitably chosen n ? 1 integers. In particular, for any positive integers p, q, where gcd(p, q) = 1, the monomial curve defined by p, q, r is a set-theoretic complete intersection for every \({r \geq pq( q - 1)}\).     

Quadratic systems with a rational first integral of degree 2: A complete classification in the coefficient space $$\mathbb{R}^{12} $$

A quadratic polynomial differential system can be identified with a single point of through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of having a rational first integral of degree 2. We show that there are only 24 topologically different phase portraits in the Poincaré disc associated to this family of quadratic systems up to a reversal of the sense of their orbits, and we provide a unique representative of every class modulo an affine change of variables and a rescalling of the time variable. Moreover, each one of these 24 representatives is determined by a set of invariant conditions and each respective first integral is given in invariant form directly in The authors are partially supported by a MEC/FEDER grant MTM2005-06098-C02-01, and a CONACIT grant number 2005SGR-00550. Partially supported by CRDF-MRDA CERIM-1006-06     

Beckman-Quarles type theorems for mappings from $$ \mathbb{R}^n $$ to $$ \mathbb{C}^n $$

Summary. Let We say that preserves the distance d 0 if for each implies Let A _n denote the set of all positive numbers d such that any map that preserves unit distance preserves also distance d. Let D _n denote the set of all positive numbers d with the property: if and then there exists a finite set S _xy with such that any map that preserves unit distance preserves also the distance between x and y. Obviously, We prove: (1) (2) for n 2 D _n is a dense subset of (2) implies that each mapping f from to (n 2) preserving unit distance preserves all distances, if f is continuous with respect to the product topologies on and      

2-Dimensional complete self-shrinkers in $$\mathbf {R}^3$$

It is our purpose to study complete self-shrinkers in Euclidean space. By making use of the generalized maximum principle for \(\mathcal {L}\)-operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in \(\mathbb R^3\). Ding and Xin (Trans Am Math Soc 366:5067–5085, 2014) have proved this result under the assumption of polynomial volume growth, which is removed in our theorem.     

Rigid Embeddings of Sasakian Hyperquadrics in $$\mathbb {C}^{n+1}$$

We give a classification of Sasakian manifolds that are CR-equivalent to hyperquadrics by describing their exact parameter space. For “ half” of the parameter space, we find an explicit representation by defining equations. This problem is related to the problem of finding pseudo-Kähler potentials with prescribed Ricci curvature.     

$$ H^{p}_{w} - L^{p}_{w} $$ Boundedness of Marcinkiewicz Integral

The Marcinkiewicz integral is essentially a Littlewood-Paley g-function, which plays a very important role in harmonic analysis. In this paper we give weaker smoothness conditions assumed on Ω to imply the boundedness of the Marcinkiewicz integral operator μ_Ω, where w belongs to the Muckenhoupt weight class.     

On Hamiltonian Minimality of Isotropic Nonhomogeneous Tori in $$\mathbb{H}^n$$ and $$\mathbb{C} \mathrm{P}^{2n+1}$$

Mathematical Notes - We construct a family of flat isotropic nonhomogeneous tori in $$\mathbb{H}^n$$ and $$\mathbb{C}\mathrm{P}^{2n+1}$$ and find necessary and sufficient conditions for their...     

Nonexistence of generalized bent functions from $$\mathbb {Z}_{2}^{n}$$ to $$\mathbb {Z}_{m}$$Zm

In this paper, several nonexistence results on generalized bent functions \(f:\mathbb {Z}_{2}^{n} \rightarrow \mathbb {Z}_{m}\) are presented by using the knowledge on cyclotomic number fields and their imaginary quadratic subfields.     

Slice-polynomial functions and twistor geometry of ruled surfaces in $$mathbb {CP}^3$$ CP 3

Mathematische Zeitschrift - In the present paper we introduce the class of slice-polynomial functions: slice regular functions defined over the quaternions, outside the real axis, whose restriction...     

Finite Factorizable Groups with $$mathbb P$$ -Subnormal $$mathrm v$$ -Supersolvable and $$mathrm{sh}$$ -Supersolvable Factors

Mathematical Notes - We study a finite factorized group $$G=AB$$ in the case when the factors $$A$$ and $$B$$ can be connected to $$G$$ by a chain of subgroups with prime indices, and either all...     

Examples of factorial threefolds complete intersection in $${\mathbb{P}^5}$$ with many singularities

Denote by ν _m (d) the maximal integer for which there exists for d >> 0{d \gg 0} a threefold X ì \mathbbP⁵{X\subset \mathbb{P}^5} complete intersection of hypersurfaces of degree respectively d and d − 1 such that X has only ordinary singularities of order m and |Sing(X)| = ν _m (d). We prove that, n_m(d) 3 j(d){\nu_m(d)\ge \varphi(d)} where j(d) ~ d⁵{\varphi(d)\sim d^5} asymptotically. This result extends (Di Gennaro and Franco in Commun Contemp Math 10(5):745–764, 2008, Corollary 2.10).     

Embedding some Riemann surfaces into $${\mathbb {C}^2}$$ with interpolation

We prove that several types of open Riemann surfaces, including the finitely connected planar domains, embed properly into such that the values on any given discrete sequence can be arbitrarily prescribed. Kutzschebauch supported by Schweizerische Nationalfonds grant 200021-107477/1.     

On the dimension of invariant measures of endomorphisms of $${\mathbb{C}\mathbb{P}^k}$$

Let f be an endomorphism of \mathbbC\mathbbP^k{\mathbb{C}\mathbb{P}^k} and ν be an f-invariant measure with positive Lyapunov exponents (λ ₁, . . . , λ _k ). We prove a lower bound for the pointwise dimension of ν in terms of the degree of f, the exponents of ν and the entropy of ν. In particular our result can be applied for the maximal entropy measure μ. When k = 2, it implies that the Hausdorff dimension of μ is estimated by dim_Hm 3 [(log d)/(l₁)] + [(log d)/(l₂)]{{\rm dim}_\mathcal{H}\mu \geq {{\rm log} d \over \lambda_1} + {{\rm log} d \over \lambda_2}}, which is half of the conjectured formula. Our method for proving these results consists in studying the distribution of the ν-generic inverse branches of f ⁿ in \mathbbC\mathbbP^k{\mathbb{C}\mathbb{P}^k} . Our tools are a volume growth estimate for the bounded holomorphic polydiscs in \mathbbC\mathbbP^k{\mathbb{C}\mathbb{P}^k} and a normalization theorem for the ν-generic inverse branches of f ⁿ .     

A note on lattice points in model domains of finite type in $${mathbb{R}^d}$$

We study the Fourier transforms of indicator functions of some special high-dimensional finite type domains and obtain estimates of the associated lattice point discrepancy.