The Kato square root problem on submanifolds
The Kato square root problem on submanifolds
复制标题
子流形上的加藤平方根问题
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Andrew J. Morris
中科院分区：
文献类型：
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作者：
Andrew J. Morris
我们解决了欧氏空间中嵌入有界第二基本形式的完备黎曼流形上散度型算子的Kato平方根问题。为此，我们证明了作用于完备黎曼流形上平凡丛上的某些一阶微分算子的扰动的局部二次估计，该完备黎曼流形的体积至多是指数增长的，并且局部Poincaré不等式成立。这是基于Axelsson、Keith和McIntosh开发的狄拉克类型运算符的框架。
We solve the Kato square root problem for divergence form operators on complete Riemannian manifolds that are embedded in Euclidean space with a bounded second fundamental form. We do this by proving local quadratic estimates for perturbations of certain first‐order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincaré inequality holds. This is based on the framework for Dirac‐type operators that was developed by Axelsson, Keith and McIntosh.