Sebastian Scholtes

activity

20122026

p

is the integral Menger curvature

M_{p}

finite for all simple polygons?

6 citations · 13 across the 7 of their papers we have counts for

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math.CA2026

A Sharp Lower Bound for Integral Menger Curvature

Sebastian Scholtes, Alexander Dohmen

We prove that round circles $C_{L}$ are the unique minimisers of integral Menger curvature among embedded closed $C^{1}$ curves $γ$ of prescribed length $L$ for every $p \geq 2$ , i.e. $…

math.CA2012

Tangency properties of sets with finite geometric curvature energies

Sebastian Scholtes

We investigate inverse thickness $1/Δ$ and the integral Menger curvature energies $U_{p}^{α}$ , $I_{p}^{α}$ and $M_{p}^{α}$ , to find that finite $1/Δ$ or $\m…

math.CA2012★ 6 cited

For which positive $p$ is the integral Menger curvature $M_{p}$ finite for all simple polygons?

Sebastian Scholtes

In this brief note we show that the integral Menger curvature $M_{p}$ is finite for all simple polygons if and only if $p \in (0, 3)$ . For the intermediate energies $\mathc…

A Sharp Lower Bound for Integral Menger Curvature

Tangency properties of sets with finite geometric curvature energies

For which positive p is the integral Menger curvature Mp​ finite for all simple polygons?

For which positive $p$ is the integral Menger curvature $M_{p}$ finite for all simple polygons?