The critical-point-theory tag has no wiki summary.

**2**

votes

**0**answers

239 views

### What is the analog of “monotonic” for scalar functions on surfaces?

"monotonic" is well defined for functions $f(x)$, where e.g. $x\in[0,1]$ and $f(x)\in\mathbb{R}$. The quality I particularly care about is that if $f(x)$ is monotonic then it will not have any local ...

**1**

vote

**0**answers

84 views

### Tubular neighborhoods in the proof of the Morse homology theorem

I have a question regarding the proof of the Morse homology theorem given by D. Salamon in "Morse theory, the Conley index and Floer homology". The full text can be found here:
...

**0**

votes

**0**answers

89 views

### Categorizing saddle points of real multivariate polynomials

I have a multivariate polynomial function of N variables
$f(x_1,x_2,…,x_N) = x_1 x_2 x_3 .. x_N \left( 1 + \sum_i^N (a_i x_i^2 - x_i) \right)$,
where $a_i > 0$ are real positive numbers.
By ...

**-1**

votes

**0**answers

89 views

### Question about Lusternik-Schnirelmann Category?

I have this sets: $\Omega\subset \mathbb{R}^N, N\geq 3$ a smooth bounded domain
$\Omega_{r}^+=\{x\in \mathbb{R}^N, d(x,\Omega)\leq r\}$ and ${\Omega}^-_{r}=\{x\in \Omega, d(x,\partial\Omega)\geq ...