论文标题
部分可观测时空混沌系统的无模型预测
Yamabe problem in the presence of singular Riemannian Foliations
论文作者
论文摘要
使用差异方法与具有正尺寸叶子的奇异riemannian叶子给出的对称性，我们证明存在Yamabe型问题的无限数量的签名改变解决方案，这些解决方案沿着叶子的叶子持续存在，并且在与这些对称性的任何其他溶液中都存在一种最小能量的溶液。特别是，我们发现与先前的结果相比，圆形球体上的Yamabe问题的标志改变解决方案，即，这些溶液沿着单一的Riemannian叶叶的叶子持续不断，这既不是由群体行动也不由等值功能引起的。为了证明这些解决方案的存在，我们证明了一种嵌入一般奇异riemannian叶子的sobolev定理，以及针对Yamabe型问题功能的相关能量的对称临界原则。
Using variational methods together with symmetries given by singular Riemannian foliations with positive dimensional leaves, we prove the existence of an infinite number of sign-changing solutions to Yamabe type problems, which are constant along the leaves of the foliation, and one positive solution of minimal energy among any other solution with these symmetries. In particular, we find sign-changing solutions to the Yamabe problem on the round sphere with new qualitative behavior when compared to previous results, that is, these solutions are constant along the leaves of a singular Riemannian foliation which is not induced neither by a group action nor by an isoparametric function. To prove the existence of these solutions, we prove a Sobolev embedding theorem for general singular Riemannian foliations, and a Principle of Symmetric Criticality for the associated energy functional to a Yamabe type problem.
