Zobrazeno 1 - 10
of 1 178
pro vyhledávání: '"53A04"'
Autor:
Miura, Tatsuya
For a class of area-preserving curvature flows of closed planar curves, we prove that every immortal solution becomes asymptotically circular without any additional assumptions on initial data. As a particular corollary, every solution of zero enclos
Externí odkaz:
http://arxiv.org/abs/2410.06183
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:
Güvenç, Şaban
In this paper, we firstly provide a concise overview of $\mathcal{S}-$manifolds, $f$-biharmonicity and $\theta _{\alpha }$-slant curves. We then derive a key equation and analyze it in detail to establish the necessary and sufficient conditions for $
Externí odkaz:
http://arxiv.org/abs/2410.04876
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
We propose an algorithm for evolving spiral curves on a planar domain by normal velocities depending on the so-called crystalline curvatures. The algorithm uses a minimizing movement approach and relies on a special level set method for embedding the
Externí odkaz:
http://arxiv.org/abs/2409.16421
Autor:
Shaw, Eve, Vellis, Vyron
An important implication of Rademacher's Differentiation Theorem is that every Lipschitz curve $\Gamma$ infinitesimally looks like a line at almost all of its points in the sense that at $\mathcal{H}^1$-almost every point of $\Gamma$, the only weak t
Externí odkaz:
http://arxiv.org/abs/2409.13662
Autor:
Miura, Tatsuya
We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.
Comment: 14 pages, 3 figu
Comment: 14 pages, 3 figu
Externí odkaz:
http://arxiv.org/abs/2409.00725
Autor:
Aithal, A R, Chorwadwala, Anisa M H
In this article, we prove that there exists a unique perimeter minimizer among all piecewise smooth simple closed curves in $M_{\kappa}^2$ enclosing area $A > 0$ $(A \leq 2{\pi}$ if ${\kappa} = 1)$, and it is a circle in $M_{\kappa}^2$ of radius $AS_
Externí odkaz:
http://arxiv.org/abs/2408.13565
Autor:
Miura, Tatsuya
This is an expository note to give a brief review of classical elastica theory, mainly prepared for giving a more detailed proof of the author's Li--Yau type inequality for self-intersecting curves in Euclidean space. We also discuss some open proble
Externí odkaz:
http://arxiv.org/abs/2408.03020
Autor:
Pausinger, Florian, Petrecca, David
We study the symmetry groups and winding numbers of planar curves obtained by taking the image of the complex unit circle under a Laurent polynomial, a class that includes weighted sums of exponentials. We generalize various results on such sums of e
Externí odkaz:
http://arxiv.org/abs/2407.09217