AI 中文总结
该研究探讨环面CR Yamabe问题，将其转化为凸多面体域上椭圆型偏微分方程边值问题，给出解的例子并证明接触环面流形可允许不同符号CR Yamabe不变量的兼容CR结构。
AI 中文摘要
我们研究共向紧接触流形上无不动点环面作用的等变CR Yamabe问题，这类例子自然出现在具有恒定标量曲率的Sasakian流形研究中。在环面情形下，我们证明该问题等价于凸多面体域上两个函数的椭圆型偏微分方程边值问题，给出了解的例子，并证明许多接触环面流形允许兼容的CR结构，其CR Yamabe不变量具有不同符号。
英文摘要
We study the equivariant CR Yamabe problem for a fixed-point-free torus action on a co-oriented compact contact manifold. Such examples arise naturally in the study of Sasakian manifolds with constant scalar curvature. In the toric case, we show that this problem is equivalent to a kind of boundary value problem for an elliptic PDE on a pair of functions defined on a convex, polyhedral domain. We provide examples of solutions and prove that many contact toric manifolds admit compatible CR structures with distinct signs of CR Yamabe invariants.
Comments33 pages, 4 figures. Comments are welcome!
