Volumes of complex analytic subvarieties of Hermitian symmetric spaces
Volumes of complex analytic subvarieties of Hermitian symmetric spaces
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埃尔米特对称空间的复解析子变体的体积
DOI：
10.1353/ajm.2002.0038
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发表时间：
2002
影响因子：
1.7
通讯作者：
W. To
中科院分区：
文献类型：
--
作者：
Jun;W. To
本文给出了n维复空间形式中具有常（正、零或负）全纯截面曲率的某些自然定义域的k维复解析子簇的体积的下界。对于每个1 ≤ k ≤ n，下界是尖锐的，因为这些界是由k维完备全测地复子流形得到的。这样的下界是通过构造对应于所涉及的Kahler度量的爆破的奇异势函数来获得的。在非紧型埃尔米特对称空间的情况下，也得到了类似的下界。在这种情况下，对于那些k值，厄米特对称空间包含k维完全全测地复子流形的下界是尖锐的，这些子流形是具有最小全纯截面曲率的复双曲空间。
We give lower bounds of volumes of k -dimensional complex analytic subvarieties of certain naturally defined domains in n -dimensional complex space forms of constant (positive, zero, or negative) holomorphic sectional curvature. For each 1 ≤ k ≤ n , the lower bounds are sharp in the sense that these bounds are attained by k -dimensional complete totally geodesic complex submanifolds. Such lower bounds are obtained by constructing singular potential functions corresponding to blow-ups of the Kahler metrics involved. Similar lower bounds are also obtained in the case of Hermitian symmetric spaces of noncompact type. In this case, the lower bounds are sharp for those values of k at which the Hermitian symmetric space contains k -dimensional complete totally geodesic complex submanifolds which are complex hyperbolic spaces of minimum holomorphic sectional curvature.