Foliations on the open $3$-ball by complete surfaces
When is a manifold a leaf of a complete closed foliation on the open unit ball? We give some answers to this question.
math.GT↗
arXiv subjects
Kazuo Masuda
Publications and source records attributed to Kazuo Masuda.
Derivatives of flat functions
We remark that there is no smooth function $f(x)$ on $[0, 1]$ which is flat at $0$ such that the derivative $f^{(n)}$ of any order $n\geq 0$ is positive on $(0,1]$. Moreover, the number of zeros of the $n$-th derivative $f^{(n)}$ grows to the infinity and the zeros accumulate to $0$ when $n \to \infty$.
math.GM↗