共查询到20条相似文献,搜索用时 15 毫秒
1.
Franki Dillen Johan Fastenakels Joeri Van der Veken Luc Vrancken 《Monatshefte für Mathematik》2007,152(2):89-96
In this article we study surfaces in
for which the unit normal makes a constant angle with the
-direction. We give a complete classification for surfaces satisfying this simple geometric condition. 相似文献
2.
Let ${\mathcal{P}_{d,n}}Let Pd,n{\mathcal{P}_{d,n}} denote the space of all real polynomials of degree at most d on
\mathbbRn{\mathbb{R}^n} . We prove a new estimate for the logarithmic measure of the sublevel set of a polynomial P ? Pd,1{P\in \mathcal{P}_{d,1}} . Using this estimate, we prove that
supP ? Pd,n| p.v.ò\mathbbRneiP(x)\fracW(x/|x|)|x|ndx| £ c log d (||W||L logL(Sn-1)+1),\mathop{\rm sup}\limits_ {P \in \mathcal{P}_{d,n}}\left| p.v.\int_{\mathbb{R}^{n}}{e^{iP(x)}}{\frac{\Omega(x/|x|)}{|x|^n}dx}\right | \leq c\,{\rm log}\,d\,(||\Omega||_L \log L(S^{n-1})+1), 相似文献
3.
In the existing theory of self-affine tiles, one knows thatthe Lebesgue measure of any integral self-affine tile correspondingto a standard digit set must be a positive integer and everyintegral self-affine tile admits some lattice Zn as a translationtiling set of Rn. In this paper, we give algorithms to evaluatethe Lebesgue measure of any such integral self-affine tile Kand to determine all of the lattice tilings of Rn by K. Moreover,we also propose and determine algorithmically another type oftranslation tiling of Rn by K, which we call natural tiling.We also provide an algorithm to decide whether or not Lebesguemeasure of the set K (K+j), jZn, is strictly positive. 相似文献
4.
Given a finite subset
of an additive group
such as
or
, we are interested in efficient covering of
by translates of
, and efficient packing of translates of
in
. A set
provides a covering if the translates
with
cover
(i.e., their union is
), and the covering will be efficient if
has small density in
. On the other hand, a set
will provide a packing if the translated sets
with
are mutually disjoint, and the packing is efficient if
has large density.
In the present part (I) we will derive some facts on these concepts when
, and give estimates for the minimal covering densities and maximal packing densities of finite sets
. In part (II) we will again deal with
, and study the behaviour of such densities under linear transformations. In part (III) we will turn to
.
Authors’ address: Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, Colorado 80309-0395,
USA
The first author was partially supported by NSF DMS 0074531. 相似文献
5.
We give simple necessary and sufficient conditions for self-affine tiles in R
2
to be homeomorphic to a disk.
Received October 10, 2000, and in revised form February 16, 2001, and April 25, 2001. Online publication July 25, 2001. 相似文献
6.
7.
Pierangelo Marcati Manuela Molinari 《NoDEA : Nonlinear Differential Equations and Applications》1999,6(2):119-132
In this paper we first prove short time existence of a classical solution for the problem which describes the evolution by
Gaussian curvature of a strictly convex hypersurface in . Then we give a proof of the existence of a viscosity solution for this problem in such a way as to define a generalized
motion existing for each time.
Received November 24, 1997 相似文献
8.
9.
Yuping Song 《Results in Mathematics》2013,63(3-4):985-998
Li and Wang (Manuscr Math 122(1):73–95, 2007) presented Laguerre geometry for hypersurfaces in ${\mathbb{R}^{n}}$ and calculated the first variational formula of the Laguerre functional by using Laguerre invariants. In this paper we present the second variational formula for Laguerre minimal hypersurfaces. As an application of this variational formula we give the standard examples of Laguerre minimal hypersurfaces in ${\mathbb{R}^{n}}$ and show that they are stable Laguerre minimal hypersurfaces. Using this second variational formula we can prove that a surface with vanishing mean curvature in ${\mathbb{R}^{3}_{0}}$ is Laguerre equivalent to a stable Laguerre minimal surface in ${\mathbb{R}^{3}}$ under the Laguerre embedding. This example of stable Laguerre minimal surface in ${\mathbb{R}^{3}}$ is different from the one Palmer gave in (Rend Mat Appl 19(2):281–293, 1999). 相似文献
10.
In this work one proves that under quite general assumptions one can deduce the topology of a bounded open set in
from an approximation of it. For this, one introduces the weak feature size (wfs) that extends for nonsmooth objects
the notion of local feature size. Our results apply to open sets with positive wfs. This class includes subanalytic open sets
which cover many cases encountered in practical applications. The proofs are based upon the study of distance functions to
closed sets and their critical points. The notion of critical point is the same as the one used in riemannian geometry [22],
[9], [20] and nonsmooth analysis [10]. As an application, one gives a way to compute the homology groups of open sets from
noisy samples of points on their boundary. 相似文献
11.
Khalifa Trimèche 《Journal of Fourier Analysis and Applications》2006,12(5):517-542
In this article we define and study the Dunkl convolution product and the Dunkl transform on spaces of distributions on
By using the main results obtained, we study the hypoelliptic Dunkl convolution equations in the space of distributions. 相似文献
12.
The nonlinear convex programming problem of finding the minimum covering weighted ball of a given finite set of points in ${\mathbb{R}^n}$ is solved by generating a finite sequence of subsets of the points and by finding the minimum covering weighted ball of each subset in the sequence until all points are covered. Each subset has at most n + 1 points and is affinely independent. The radii of the covering weighted balls are strictly increasing. The minimum covering weighted ball of each subset is found by using a directional search along either a ray or a circular arc, starting at the solution to the previous subset. The step size is computed explicitly at each iteration. 相似文献
13.
14.
Yuxiang Li Yong Luo Hongyan Tang 《Calculus of Variations and Partial Differential Equations》2013,46(1-2):31-37
Let f be a conformal map from the 2-disk into ${\mathbb{R}^n}$ . We prove that the image f(B) have a normal tangent vector basis (e 1, e 2) with ${\|d(e_{1}, e_{2})\|_{L^2(B)} \leq C\|A\|_{L^2(B)}}$ when the total Gauss curvature ${\int_B |K_{f}| d\mu_f < 2\pi}$ . 相似文献
15.
We show that the combinatorial complexity of a single cell in an arrangement of k convex polyhedra in 3-space having n facets
in total is
, for any
, thus settling a conjecture of Aronov et al. We then extend our analysis and show that the overall complexity of the zone
of a low-degree
algebraic surface, or of the boundary of an arbitrary convex set, in an arrangement of k convex polyhedra in 3-space with
n facets in total, is also
, for any
. Finally, we present a deterministic algorithm that constructs a single cell in an arrangement of this kind, in time
, for any
. 相似文献
16.
Josè L. Gámez 《NoDEA : Nonlinear Differential Equations and Applications》1997,4(3):341-357
Existence of positive solutions of a semilinear elliptic problem on , arising from population genetics is obtained. We use an approximation procedure, by accumulation of branches of solutions
of the problem stated on balls of sufficiently large radia.
Received January 19, 1996 相似文献
17.
The main purpose of this paper is to investigate positive solutions of the following system of integral equations with weight Riesz potential on Ω: $$\left\{\begin{array}{ll} u(x)=\int\limits_{\Omega}{|x|^{-\alpha}|x-y|^{-\mu}|y|^{-\beta}}{u^a(y)v^b(y)}dy,\\ v(x)=\int\limits_{\Omega}{|x|^{-\gamma}|x-y|^{-\nu}|y|^{-\kappa}}{u^c(y)v^d(y)}dy,\\ \end{array} \right.$$ where a, b, c, d, α, β, γ, κ, μ, ν are constants. With the method of moving planes, we establish the symmetry of both the solution and the bounded C 1 domain Ω if u and v are constants on ?Ω. Moreover, we also give a symmetry result for systems of integral equations with weight Riesz potential on exterior domains. 相似文献
18.
《复变函数与椭圆型方程》2012,57(1):69-81
We consider the generalization of linear fractional transformations of the plane to $ {\shadC}^n $ . Analogs of the one-variable theory are developed including fixed point sets and points of symmetry. The domains in $ {\shadC}^n $ that are images of the ball under these transformations are found. Finally, we see some examples where classical fixed point results follow from this theory in a natural way. 相似文献
19.
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 \({r \geq pq( q - 1)}\). 相似文献
20.
Genqian Liu 《Calculus of Variations and Partial Differential Equations》2013,47(3-4):567-588
In this paper, we obtain the sharp k-th order Sobolev inequalities in the hyperbolic space ${\mathbb{H}^n}$ for all k = 1, 2, 3, . . . . This gives an answer to an open question raised by Aubin in [Aubin, Princeton University Press, Princeton (1982), pp. 176–177] for ${W^{k,2}(\mathbb{H}^n)}$ with k > 1. In addition, we prove that the associated Sobolev constants are optimal. 相似文献
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