Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Pampano, Alvaro"'
For every $p\in\mathbb{R}$, we study $p$-elastic curves in the hyperbolic plane $\mathbb{H}^2$ and in the de Sitter $2$-space $\mathbb{H}_1^2$. We analyze the existence of closed $p$-elastic curves with nonconstant curvature showing that in the hyper
Externí odkaz:
http://arxiv.org/abs/2404.08593
Autor:
Palmer, Bennett, Pampano, Alvaro
In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this paper we develop and apply a second variation formula for the Helfric
Externí odkaz:
http://arxiv.org/abs/2401.05285
Autor:
Musso, Emilio, Pampano, Alvaro
We provide a geometric transformation on null curves in the anti-de Sitter $3$-space (AdS) which induces the B\"{a}cklund transformation for the KdV equation. In addition, we show that this geometric transformation satisfies a suitable permutability
Externí odkaz:
http://arxiv.org/abs/2312.10765
Autor:
Musso, Emilio, Pampano, Alvaro
We formulate integrable flows related to the KdV hierarchy on null curves in the anti-de Sitter 3-space (${\rm AdS}$). Exploiting the specific properties of the geometry of ${\rm AdS}$, we analyze their interrelationships with Pinkall flows in centro
Externí odkaz:
http://arxiv.org/abs/2311.11137
Autor:
Musso, Emilio, Pampano, Alvaro
We study critical trajectories in the hyperbolic plane for the $1/2$-Bernoulli's bending energy with length constraint. Critical trajectories with periodic curvature are classified into three different types according to the causal character of their
Externí odkaz:
http://arxiv.org/abs/2302.03378
Autor:
Pampano, Alvaro
We study translating soliton solutions to the flow by powers of the curvature of curves in the plane. We characterize these solitons as critical curves for functionals depending on the curvature. More precisely, translating solitons to the flow by po
Externí odkaz:
http://arxiv.org/abs/2211.04603
For $p\in\mathbb{R}$, we show that non-circular closed $p$-elastic curves in $\mathbb{S}^2$ exist only when $p=2$, in which case they are classical elastic curves, or when $p\in(0,1)$. In the latter case, we prove that for every pair of relatively pr
Externí odkaz:
http://arxiv.org/abs/2209.11597
Autor:
Palmer, Bennett, Pampano, Alvaro
We use a bifurcation theory due to Crandall and Rabinowitz to show the existence of a symmetry breaking bifurcation of a specific one parameter family of axially symmetric disc type solutions of a membrane equation with fixed boundary. In place of wo
Externí odkaz:
http://arxiv.org/abs/2206.10971
Autor:
López, Rafael, Pámpano, Álvaro
Publikováno v:
Journal of Geometry and Physics, (2022), 104731
This paper considers the energies of three different physical scenarios and obtains relations between them in a particular case. The first family of energies consists of the Willmore-type energies involving the integral of powers of the mean curvatur
Externí odkaz:
http://arxiv.org/abs/2206.01070
Autor:
Musso, Emilio, Pampano, Alvaro
We study critical trajectories in the sphere for the $1/2$-Bernoulli's bending functional with length constraint. For every Lagrange multiplier encoding the conservation of the length during the variation, we show the existence of infinitely many clo
Externí odkaz:
http://arxiv.org/abs/2204.01096