论文标题
围绕强烈的Viterbo猜想的例子
Examples around the strong Viterbo conjecture
论文作者
论文摘要
Viterbo的猜想的强大版本断言，所有归一化的符号能力都同意凸域。我们回顾了已知的结果，表明某些特定的归一化符号能力在凸形域中一致。我们还回顾了为什么所有标准化的符号能力都同意$ s^1 $ invariant凸域。我们介绍了一个新的示例，称为“单调折叠域”，这些示例不一定是凸面，并且在四个维度上包括所有动态凸出圆形圆环域。我们证明，对于在四个维度上的单调感谢您的域，所有标准化的符号能力都同意。对于任意维度的单调折叠域，我们证明了Gromov宽度与第一个模棱两可的能力一致。我们还研究了一个非符号旋转型域的例子，并确定何时在这些示例中得出强烈的Viterbo猜想的结论。在途中，我们计算了四个维度的大型“弱凸形圆环域”的圆柱能力。
A strong version of a conjecture of Viterbo asserts that all normalized symplectic capacities agree on convex domains. We review known results showing that certain specific normalized symplectic capacities agree on convex domains. We also review why all normalized symplectic capacities agree on $S^1$-invariant convex domains. We introduce a new class of examples called "monotone toric domains", which are not necessarily convex, and which include all dynamically convex toric domains in four dimensions. We prove that for monotone toric domains in four dimensions, all normalized symplectic capacities agree. For monotone toric domains in arbitrary dimension, we prove that the Gromov width agrees with the first equivariant capacity. We also study a family of examples of non-monotone toric domains and determine when the conclusion of the strong Viterbo conjecture holds for these examples. Along the way we compute the cylindrical capacity of a large class of "weakly convex toric domains" in four dimensions.
