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1.
单叶调和映射   总被引:3,自引:0,他引:3  
张玉林 《数学进展》1993,22(5):402-410
由于在极小曲面理论中的作用,对调和映射的研究已有较长时间。1984年以来,经典解析单叶映射的理论被推广至调和单叶映射,并获得许多结论。这些工作引起人们对它的浓厚兴趣。该文介绍这一课题某些重要成果的概貌,并指出一些尚未解决的问题。它共分六个部分:映射定理;单叶调和函数的数值估计;特殊映射;变分方法;境界性质和在极小曲面中的应用。  相似文献
2.
解析函数模的下界问题   总被引:2,自引:1,他引:1  
给出了在|z|<R中含有零点的解析函数的模的一个下界;其推论推广了[4]的Thm.1,由此可较易地推出[5]中关于单位圆盘上解析函数的加权代数的可除性问题的结论.  相似文献
3.
Let Ω be a bounded domain with smooth boundary in . For the more general weight b, some nonlinearities f and singularities g, by two kinds of nonlinear transformations, a new perturbation method, which was introduced by García Melián in [J. García Melián, Boundary behavior of large solutions to elliptic equations with singular weights, Nonlinear Anal. 67 (2007) 818–826], and comparison principles, we show that the boundary behavior of solutions to a boundary blow-up elliptic problem Δw=b(x)f(w),w>0,xΩ,w|Ω= and a singular Dirichlet problem −Δu=b(x)g(u),u>0,xΩ,u|Ω=0 has the same form under the nonlinear transformations, which can be determined in terms of the inverses of the transformations.  相似文献
4.
半空间中一类次调和函数的增长性质   总被引:1,自引:1,他引:0       下载免费PDF全文
张艳慧  邓冠铁 《数学学报》2008,51(2):319-326
在Rn的半空间{x∈Rn,xn>0}中,得到了具有Dirichlet数据的Poisson积分在自然的积分收敛条件下满足增长性质u(x)=o(|x|),这里|x|→∞,这一性质对于半空间中满足一定条件的次调和函数仍然成立.该结果把复平面C中解析函数的增长性质推广到了n-维Euclidean半空间,并且推广了n-维Euclidean半空间中某些经典的结果.  相似文献
5.
We discuss some problems on rigidity of canonical realizations of complex homogeneous domains at Cn  相似文献
6.
The classical Beurling-Nevanlinna upper bound for subharmonic functions is extended to subsolutions of the stationary Schrödinger equation.

  相似文献

7.
We prove a Littlewood-type theorem which shows the sharpness of the Korányi approach region for the boundary behavior of Poisson-Szegö integrals on the unit ball of . Our result is stronger than Hakim and Sibony (1983).

  相似文献

8.

We obtain a sharp asymptotic relation between the infimum and the maximum on a circle of a subharmonic function of zero lower order. An example is constructed, which shows the sharpness of the relation in the class of entire functions of zero order such that , where as .

  相似文献

9.
A subset of the -dimensional torus is called a set of uniqueness, or -set, if every multiple trigonometric series spherically converging to outside vanishes identically. We show that all countable sets are -sets and also that sets are -sets for every . In particular, , where is the Cantor set, is an set and hence a -set. We will say that is a -set if every multiple trigonometric series spherically Abel summable to outside and having certain growth restrictions on its coefficients vanishes identically. The above-mentioned results hold also for sets. In addition, every -set has measure , and a countable union of closed -sets is a -set.

  相似文献

10.

Let be the Weinstein operator on the half space, . Suppose there is a sequence of Borel sets such that a certain tangential projection of onto forms a pairwise disjoint subset of the boundary. Let be a finite test measure on the boundary for a specific non-isotropic Hausdorff measure. The measure is carried back to a measure on a subset of by the projection. We give an upper bound for the Weinstein potential corresponding to the measure in terms of a universal constant and a Weinstein subharmonic function. We use this upper bound to deduce a result concerning tangential behavior of Weinstein potentials at the boundary with the exception of sets on the boundary of vanishing non-isotropic Hausdorff measure.

  相似文献

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