Limiting behavior of a class of Hermitian Yang-Mills metrics, I
Limiting behavior of a class of Hermitian Yang-Mills metrics, I
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一类 Hermitian Yang-Mills 度量的极限行为，I
DOI：
10.1007/s11425-019-9512-6
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发表时间：
2019-11-01
影响因子：
1.4
通讯作者：
Fu, Jixiang
中科院分区：
文献类型：
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作者：
Fu, Jixiang
本文研究了两条椭圆曲线乘积上一类二阶斜率稳定向量丛上的Hermitian Yang-Mills度量族在Kahler度量Ω（Ω）= Ω-> 0时的极限行为.这里，Ω（Ω）是平坦的，并且在两条椭圆曲线上分别具有面积Ω和Ω（-）（1）。显式构造了向量丛上的一类Hermitian度量，并对HYM度量进行了归一化。然后，我们比较家庭的归一化HYM度量与家庭的构造厄米特度量做估计。只要给出C-0-估计，就可以得到高阶估计.我们还得到了C-0-范数下界的估计。如果可以得到C-0范数上界的期望估计，则可以证明这两类度量在任何C-k范数下都接近于任意阶。
This paper begins to study the limiting behavior of a family of Hermitian Yang-Mills (HYM for brevity) metrics on a class of rank two slope stable vector bundles over a product of two elliptic curves with Kahler metrics omega (epsilon) when epsilon -> 0. Here, omega (epsilon) are flat and have areas epsilon and epsilon (-)(1) on the two elliptic curves, respectively. A family of Hermitian metrics on the vector bundle are explicitly constructed and with respect to them, the HYM metrics are normalized. We then compare the family of normalized HYM metrics with the family of constructed Hermitian metrics by doing estimates. We get the higher order estimates as long as the C-0-estimate is provided. We also get the estimate of the lower bound of the C-0-norm. If the desired estimate of the upper bound of the C-0-norm can be obtained, then it would be shown that these two families of metrics are close to arbitrary order in epsilon in any C-k norms.