排序方式: 共有8条查询结果,搜索用时 31 毫秒
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《复变函数与椭圆型方程》2012,57(1):73-79
If u is a sufficiently smooth maximal plurisubharmonic function such that the complex Hessian of u has constant rank, it is known that there exists a foliation by complex manifolds, such that u is harmonic along the leaves of the foliation. In this paper, we show a partial analogue of this result for maximal plurisubharmonic functions that are merely continuous, without the assumption on the complex Hessian. In this setting, we cannot expect a foliation by complex manifolds, but we prove the existence of positive currents of bidimension (1, 1) such that the function is harmonic along the currents. 相似文献
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《复变函数与椭圆型方程》2012,57(5):393-408
This paper investigates the polynomial convexity of subsets of the two-torus. Given a compact subset K of T 2 , we find regions in K which do not contribute to the polynomial hull of K inside the bidisc. 相似文献
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《复变函数与椭圆型方程》2012,57(11):981-1001
The problem of approximating singularity sets by analytic varieties has been considered by several authors. The present work deals with singularity sets projecting over a finitely connected domain. The results obtained in these cases allow us to prove the existence of a Riemann surface in a neighborhood of a two-sheeted singularity set. 相似文献
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《Optimization》2012,61(1-4):309-341
Let Xbe a setW set of extended-real valued functions on Xand 0 an element of Xsuch that w(0) = 0 for all win W. We give a general theory of dual representations, without any extra parameters, of various hulls for extended-real valued functions on X satisfying f(0)= inf f(X\{0})We use the unifying framework of quasi-convex functions with respect to families of subsets of Xand a condition generalizing the bipolar theorem. Our results contain, as particular cases, some recent results of Thach (1991, 1993) and Rubinov and Glover (1996) on W-pseudo-affine and W-quasi-coaffine hulls.We also give some results in the converse direction. These yield, in particular, that the bipolar theorem is equivalent to a certain property of the lower semi-continuous quasi-convex hulls of functions on locally convex spaces 相似文献
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