论文标题
严格凸出的射击歧管的特侧刚性
Entropy rigidity for foliations by strictly convex projective manifolds
论文作者
论文摘要
让$ n $是一个紧凑型歧管，带有叶子$ \ mathscr {f} _n $，其叶子是紧凑的严格凸出凸出歧管。令$ m $成为一个紧凑的歧管，带有叶子$ \ mathscr {f} _m $，其叶子是紧凑的尺寸紧凑的双曲线歧管，其尺寸大于或等于$ 3 $。假设有一个叶状的同构$ f：（n，\ mathscr {f} _n）\ rightArrow（m，\ m m缩{f} _m）$，当限制为叶子时，它是$ c^1 $ regular。在以前的情况下，存在一个明确定义的叶卷熵的概念$ h（n，\ mathscr {f} _n）$和$ h（m，\ mathscr {f} _m）$，并且它保留$ h（m，\ m m m马理{f} {f} _m _m）另外，如果平等成立，则叶子必须是同性恋的。
Let $N$ be a compact manifold with a foliation $\mathscr{F}_N$ whose leaves are compact strictly convex projective manifolds. Let $M$ be a compact manifold with a foliation $\mathscr{F}_M$ whose leaves are compact hyperbolic manifolds of dimension bigger than or equal to $3$. Suppose to have a foliation-preserving homeomorphism $f:(N,\mathscr{F}_N) \rightarrow (M,\mathscr{F}_M)$ which is $C^1$-regular when restricted to leaves. In the previous situation there exists a well-defined notion of foliated volume entropies $h(N,\mathscr{F}_N)$ and $h(M,\mathscr{F}_M)$ and it holds $h(M,\mathscr{F}_M) \leq h(N,\mathscr{F}_N)$. Additionally, if equality holds, then the leaves must be homothetic.
