Zobrazeno 1 - 10
of 23
pro vyhledávání: '"58B20, 58D05"'
Publikováno v:
Journal of Nonlinear Science (2022) 32:17
We show that two families of equations on the real line, the generalized inviscid Proudman--Johnson equation, and the $r$-Hunter--Saxton equation (recently introduced by Cotter et al.) coincide for a certain range of parameters. This gives a new geom
Externí odkaz:
http://arxiv.org/abs/2101.03601
Autor:
Jerrard, Robert L., Maor, Cy
Publikováno v:
Ann Glob Anal Geom (2019) 56 : 351--360
We study the geodesic distance induced by right-invariant metrics on the group $\operatorname{Diff}_c(M)$ of compactly supported diffeomorphisms of a manifold $M$, and show that it vanishes for the critical Sobolev norms $W^{s,n/s}$, where $n$ is the
Externí odkaz:
http://arxiv.org/abs/1901.04121
Autor:
Jerrard, Robert L., Maor, Cy
Publikováno v:
Ann Glob Anal Geom (2019) 55: 631--656
We study the geodesic distance induced by right-invariant metrics on the group $\operatorname{Diff}_\text{c}(M)$ of compactly supported diffeomorphisms, for various Sobolev norms $W^{s,p}$. Our main result is that the geodesic distance vanishes ident
Externí odkaz:
http://arxiv.org/abs/1805.01410
Publikováno v:
Geometry, Imaging and Computing, Volume 1, Number 1, 1-56, 2014
We consider spaces of smooth immersed plane curves (modulo translations and/or rotations), equipped with reparameterization invariant weak Riemannian metrics involving second derivatives. This includes the full $H^2$-metric without zero order terms.
Externí odkaz:
http://arxiv.org/abs/1311.3526
Publikováno v:
Annals of Global Analysis and Geometry 44, 4 (2013), 361-368
The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold $M$ of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric $H^s$ of order $0\le s<\tfrac12
Externí odkaz:
http://arxiv.org/abs/1211.7254
Autor:
Mumford, David, Michor, Peter W.
Publikováno v:
Journal of Geometric Mechanics 5, 3 (2013), 319-344
We study a family of approximations to Euler's equation depending on two parameters $\varepsilon,\eta \ge 0$. When $\varepsilon=\eta=0$ we have Euler's equation and when both are positive we have instances of the class of integro-differential equatio
Externí odkaz:
http://arxiv.org/abs/1209.6576
Publikováno v:
Journal of Nonlinear Science 24, 5 (2014), 769-808
In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space $\operatorname{Diff}_{1}(\mathbb R)$ equipped with the homogenous Sobolev metric of order one is a flat space in the sense of Rie
Externí odkaz:
http://arxiv.org/abs/1209.2836
Autor:
Bruveris, Martins
Publikováno v:
Ann. Glob. Anal. Geom., 41(4), 461-472, 2012
The geodesic equation for the right invariant $L^2$-metric (which is a weak Riemannian metric) on each Virasoro-Bott group is equivalent to the KdV-equation. We prove that the corresponding energy functional, when restricted to paths with fixed endpo
Externí odkaz:
http://arxiv.org/abs/1106.4326
Publikováno v:
Ann. Glob. Anal. Geom. 44, 1 (2013), 5-21
We study Sobolev-type metrics of fractional order $s\geq0$ on the group $\Diff_c(M)$ of compactly supported diffeomorphisms of a manifold $M$. We show that for the important special case $M=S^1$ the geodesic distance on $\Diff_c(S^1)$ vanishes if and
Externí odkaz:
http://arxiv.org/abs/1105.0327
Publikováno v:
Ann. Glob. Anal. Geom. 41, 4 (2012) 461-472
The Virasoro-Bott group endowed with the right-invariant $L^2$-metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.
Comment: 10 pages, 1 figure; ty
Comment: 10 pages, 1 figure; ty
Externí odkaz:
http://arxiv.org/abs/1102.0236