共查询到20条相似文献,搜索用时 15 毫秒
1.
Let
be the unit disk of the complex plane. A conformai map of
into itself is called hyperbolically convex if the non-Euclidean segment between any two points of
also belongs to
. In this paper we prove several inequalities that are analogous to inequalities about (Euclidean) convex univalent functions.
We show that if ƒ (0) = 0, then Re zf′/f > 1/2. This inequality is the key for the results of this paper. In particular we
deduce a three-variable inequality corresponding to that of Ruscheweyh and Sheil-Small. The sharp bound for the Schwarzian
derivative remains open. 相似文献
2.
Nahum Zobin 《Journal of Geometric Analysis》1999,9(3):491-511
Consider the Sobolev space W
∞
k
(Ω) of functions with bounded kth derivatives defined in a planar domain. We study the problem of extendability of functions
from W
∞
k
(Ω) to the whole ℝ2 with preservation of class, i.e., surjectivity of the restriction operator W
∞
k
(ℝ2) → W
∞
k
(Ω). 相似文献
3.
We characterize the Besov-Lipschitz spaces with zero boundary conditions on bounded smooth domains. We prove that the appropriate
first and second difference norms are equivalent to the norm given in terms of the transition kernel of the Brownian motion
killed upon exit from the domain. 相似文献
4.
Chiung-Jue Sung 《Journal of Geometric Analysis》1998,8(1):143-161
Given a complete Riemannian manifold (M, g) with nonnegative sectional curvature outside a compact subset. Let h be another
Riemannian metric which is uniformly equivalent to g. It was shown that the dimension of the space of bounded harmonic functions
on (M, h) is finite and is the same as of that under metric g, and the dimension of the space spanned by nonnegative harmonic
functions on (M, h) is also finite and is the same as of that under metric g. Moreover, bases were constructed for both spaces
on (M, h) and precise estimates were established on the asymptotic behavior at infinity for those basic functions. 相似文献
5.
First-order regularity of convex functions on Carnot Groups 总被引:1,自引:0,他引:1
Matthieu Rickly 《Journal of Geometric Analysis》2006,16(4):679-702
We prove that h-convex functions on Carnot groups of step two are locally Lipschitz continuous with respect to any intrinsic
metric. We show that an additional measurability condition implies the local Lipschitz continuity of h-convex functions on
arbitrary Carnot groups.
To the Memory of Q. G. 相似文献
6.
In this article we prove that bounded Hua-harmonic functions on tube domains that satisfy some boundary regularity condition
are necessarily pluriharmonic. In doing so, we show that a similar theorem is true on one-dimensional extensions of the Heisenberg
group or equivalently on the Siegel upper half-plane. 相似文献
7.
R. Monneau 《Journal of Geometric Analysis》2003,13(2):359-389
We study the obstacle problem in two dimensions. On the one hand we improve a result of L.A. Caffarelli and N.M. Rivière:
we state that every connected component of the interior of the coincidence set has at most N
0
singular points, where N
0
is only dependent on some geometric constants. Moreover, if the component is small enough, then this component has at most
two singular points. On the other hand, we prove in a simple case a conjecture of D.G. Schaeffer on the generic regularity
of the free boundary: for a family of obstacle problems in two dimensions continuously indexed by a parameter λ, the free
boundary of the solution uλ is analytic for almost every λ. Finally we present a new monotonicity formula for singular points.
Dedicated to Henri Berestycki and Alexis Bonnet. 相似文献
8.
Anna Siano 《Journal of Geometric Analysis》2007,17(3):547-557
We construct explicit supporting manifolds and local holomorphic peak functions as obstructions to the extendability of holomorphic
functions on a class of domains not necessarily pseudoconvex in CN, N >2. 相似文献
9.
10.
We prove smoothness of strictly Levi convex solutions to the Levi equation in several complex variables. This equation is
fully non linear and naturally arises in the study of real hypersurfaces in ℂn+1, for n ≥ 2. For a particular choice of the right-hand side, our equation has the meaning of total Levi curvature of a real
hypersurface ℂn+1 and it is the analogous of the equation with prescribed Gauss curvature for the complex structure. However, it is degenerate
elliptic also if restricted to strictly Levi convex functions. This basic failure does not allow us to use elliptic techniques
such in the classical real and complex Monge-Ampère equations. By taking into account the natural geometry of the problem
we prove that first order intrinsic derivatives of strictly Levi convex solutions satisfy a good equation. The smoothness
of solutions is then achieved by mean of a bootstrap argument in tangent directions to the hypersurface. 相似文献
11.
Georgios Alexopoulos 《Journal of Geometric Analysis》2000,10(2):207-218
We prove an analog of the Berry-Esseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic
coefficients. As an application of this result, we prove the Lp boundedness of the associated Riesz transform operators. 相似文献
12.
Qing Han 《Journal of Geometric Analysis》2000,10(3):455-480
In this paper we first give a priori estimates on asymptotic polynomials of solutions to elliptic equations at nodal points.
This leads to a pointwise version of Schauder estimates. As an application we discuss the structure of nodal sets of solutions
to elliptic equations with nonsmooth coefficients. 相似文献
13.
Existence of positive weak solutions with a prescribed singular set of semilinear elliptic equations
In this paper, we consider the problem of the existence of non-negative weak solution u of
having a given closed set S as its singular set. We prove that when
and S is a closed subset of Ω, then there are infinite many positive weak solutions with S as their singular set. Applying
this method to the conformal scalar curvature equation for n ≥ 9, we construct a weak solution
of
such that Sn is the singular set of u where L0 is the conformal Laplacian with respect to the standard metric of Sn. When n = 4 or 6, this kind of solution has been constructed by Pacard. 相似文献
14.
Existence of solution for semilinear problem with the Laplace-Beltrami operator on non-compact Riemannian manifolds with rich
symmetries is proved by concentration compactness based on actions of the manifold's isometry group. 相似文献
15.
In this paper a unique continuation result is proved for differential inequality of second order. 相似文献
16.
J. M. Aldaz 《Rendiconti del Circolo Matematico di Palermo》2001,50(1):213-216
We show that given any Borel measure onR, every Lipschitz function is μ-a.e. differentiable with respect to μ. 相似文献
17.
We consider the harmonic extension AN of an H-type group N with Lie algebra n = v + z, and [v, v] = z. We characterize the
positive definite spherical functions on AN. 相似文献
18.
Christine M. Guenther 《Journal of Geometric Analysis》2002,12(3):425-436
In this article we prove the existence of a fundamental solution for the linear parabolic operator L(u) = (Δ − ∂/∂t − h)u,
on a compact n-dimensional manifold M with a time-parameterized family of smooth Riemannian metrics g(t). Δ is the time-dependent
Laplacian based on g(t), and h(x, t) is smooth. Uniqueness, positivity, the adjoint property, and the semigroup property hold.
We further derive a Harnack inequality for positive solutions of L(u) = 0 on (M, g(t) on a time interval depending on curvature
bounds and the dimension of M, and in the special case of Ricci flow, use it to find lower bounds on the fundamental solution
of the heat operator in terms of geometric data and an explicit Euclidean type heat kernel. 相似文献
19.
20.
For any positive real numbers A, B, and d satisfying the conditions
, d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫ℝ|g(x)|2(1+|x|
A
)/log
d
(2+|x|)dx < ∞ and
. 相似文献