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pro vyhledávání: '"primary 53a04"'
Autor:
Miura, Tatsuya
We solve a variant of Huisken's problem for open curves: we construct migrating elastic flows under the natural boundary conditions, extending previous work from the nonlocal flow to the purely local flow.
Comment: 8 pages, 1 figure
Comment: 8 pages, 1 figure
Externí odkaz:
http://arxiv.org/abs/2411.03751
Autor:
Ghomi, Mohammad, Raffaelli, Matteo
We prove that curves of constant torsion satisfy the $C^1$-dense h-principle in the space of immersed curves in Euclidean space. In particular, there exists a knot of constant torsion in each isotopy class. Our methods, which involve convex integrati
Externí odkaz:
http://arxiv.org/abs/2410.06027
Autor:
Müller, Marius, Yoshizawa, Kensuke
This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit parametrization. The classification strongly depends on a special pena
Externí odkaz:
http://arxiv.org/abs/2409.17877
Autor:
Ghomi, Mohammad, Raffaelli, Matteo
We prove that curves of constant curvature satisfy the parametric $C^1$-dense relative $h$-principle in the space of immersed curves with nonvanishing curvature in Euclidean space $R^{n\geq 3}$. It follows that two knots of constant curvature in $R^3
Externí odkaz:
http://arxiv.org/abs/2407.01729
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and total torsion while simultaneously allowing for a variable bending stiffness along the arc-length of the curve.
Externí odkaz:
http://arxiv.org/abs/2404.04027
In this paper, we give a generalization of Fenchel's theorem for closed curves as frontals in Euclidean space $\mathbb{R}^n$. We prove that, for a non-co-orientable closed frontal in $\mathbb{R}^n$, its total absolute curvature is greater than or equ
Externí odkaz:
http://arxiv.org/abs/2403.00487
Autor:
Kemmochi, Tomoya, Miura, Tatsuya
Publikováno v:
J. Math. Pures Appl. 185 (2024), 47--62
Huisken's problem asks whether there is an elastic flow of closed planar curves that is initially contained in the upper half-plane but `migrates' to the lower half-plane at a positive time. Here we consider variants of Huisken's problem for open cur
Externí odkaz:
http://arxiv.org/abs/2303.12516
We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an application in the
Externí odkaz:
http://arxiv.org/abs/2303.08043
Autor:
Ghomi, Mohammad, Wenk, James
We show that in Euclidean 3-space any closed curve $\gamma$ which contains the unit sphere within its convex hull has length $L\geq4\pi$, and characterize the case of equality. This result generalizes the authors' recent solution to a conjecture of Z
Externí odkaz:
http://arxiv.org/abs/2209.05988
Autor:
Shonkwiler, Clayton
Publikováno v:
Journal of Knot Theory and Its Ramifications 31 (2022), no. 10, 2250063
Previous work used polygonal realizations of knots to reduce the problem of computing the superbridge number of a realization to a linear programming problem, leading to new sharp upper bounds on the superbridge index of a number of knots. The presen
Externí odkaz:
http://arxiv.org/abs/2206.06950