Zobrazeno 1 - 10
of 67
pro vyhledávání: '"RAFFAELLI, Matteo"'
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:
Raffaelli, Matteo
Given a smooth $s$-dimensional submanifold $S$ of $\mathbb{R}^{m+c}$ and a smooth distribution $\mathcal{D}\supset TS$ of rank $m$ along $S$, we study the following geometric Cauchy problem: to find an $m$-dimensional rank-$s$ submanifold $M$ of $\ma
Externí odkaz:
http://arxiv.org/abs/2409.04358
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
Autor:
Raffaelli, Matteo
Publikováno v:
Geom. Dedicata 217 (2023), no. 6, Paper No. 96
A curve $\gamma$ in a Riemannian manifold $M$ is three-dimensional if its torsion (signed second curvature function) is well-defined and all higher-order curvatures vanish identically. In particular, when $\gamma$ lies on an oriented hypersurface $S$
Externí odkaz:
http://arxiv.org/abs/2308.12684
Autor:
Blatt, Simon, Raffaelli, Matteo
Publikováno v:
J. Geom. Anal. 34 (2024), no. 8, Paper No. 250
We apply the direct method of the calculus of variations to show that any nonplanar Frenet curve in $\mathbb{R}^{3}$ can be extended to an infinitely narrow flat ribbon having minimal bending energy. We also show that, in general, minimizers are not
Externí odkaz:
http://arxiv.org/abs/2307.07311
Publikováno v:
Math. Intelligencer 46 (2024), no. 1, 9-21
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified treatment, complemented with several novel observations, may be useful. Th
Externí odkaz:
http://arxiv.org/abs/2212.09716
Autor:
Raffaelli, Matteo
Publikováno v:
Results Math. 78 (2023), no. 6, Paper No. 208
We study ruled submanifolds of Euclidean space. First, to each (parametrized) ruled submanifold $\sigma$, we associate an integer-valued function, called degree, measuring the extent to which $\sigma$ fails to be cylindrical. In particular, we show t
Externí odkaz:
http://arxiv.org/abs/2209.00888
Autor:
Markvorsen, Steen, Raffaelli, Matteo
Publikováno v:
J. Geom. Anal. 34 (2024), no. 2, Paper No. 53
We study totally umbilic isometric immersions between Riemannian manifolds. First, we provide a novel characterization of the totally umbilic isometric immersions with parallel normalized mean curvature vector, i.e., those having nonzero mean curvatu
Externí odkaz:
http://arxiv.org/abs/2107.10087
Autor:
Raffaelli, Matteo
Publikováno v:
Proc. Roy. Soc. Edinburgh Sect. A 153 (2023), no. 4, 1297-1314
We study ribbons of vanishing Gaussian curvature, i.e., flat ribbons, constructed along a curve in $\mathbb{R}^{3}$. In particular, we first investigate to which extent the ruled structure determines a flat ribbon: in other words, we ask whether for
Externí odkaz:
http://arxiv.org/abs/2104.12382