The Exponential Map of the Group of Area-Preserving Diffeomorphisms of a Surface with Boundary

被引：3

作者：

Benn, James ^{[1
]}

Misiolek, Gerard ^{[2
]}

Preston, Stephen C. ^{[3
,4
]}

机构：

[1] Massey Univ, 3 Hardie St, Palmerston North, New Zealand

[2] Notre Dame Univ, Dept Math, 255 Hurley, Notre Dame, IN 46656 USA

[3] CUNY Brooklyn Coll, Dept Math, Room 1156,Ingersoll Hall,2900 Bedford Ave, Brooklyn, NY 11210 USA

[4] CUNY, Grad Ctr, Room 1156,Ingersoll Hall,2900 Bedford Ave, Brooklyn, NY 11210 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2018年 / 229卷 / 03期

关键词：

VOLUMORPHISM GROUP; CONJUGATE-POINTS; EULER EQUATIONS; FLUID; FLOWS;

D O I：

10.1007/s00205-018-1231-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the Riemannian exponential map of the right-invariant L (2) metric on the group of volume-preserving diffeomorphisms of a two-dimensional manifold with a nonempty boundary is a nonlinear Fredholm map of index zero.

引用

页码：1015 / 1035

页数：21

共 21 条

[1]

Arnold V.I., 2014, DIFFERENTIAL GEOMETR, V2

[2]

Arnold VI, 1998, Topological methods in hydrodynamics

[3]

Benn J., 2014, THESIS

[4]

Benn J., 2016, ARNOLD MATH J, V2, P249

[5] Conjugate points on the symplectomorphism group [J].

Benn, James .

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2015, 48 (02) :133-147

[6] Singularities of the exponential map on the volume-preserving diffeomorphism group [J].

Ebin, D. G. ;

Misiolek, G. ;

Preston, S. C. .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2006, 16 (04) :850-868

[7] GROUPS OF DIFFEOMORPHISMS AND MOTION OF AN INCOMPRESSIBLE FLUID [J].

EBIN, DG ;

MARSDEN, J .

ANNALS OF MATHEMATICS, 1970, 92 (01) :102-&

[8] HILBERT MANIFOLDS WITHOUT EPICONJUGATE POINTS [J].

GROSSMAN, N .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 16 (06) :1365-&

[9]

Kato T., 1966, PERTURBATION THEORY, P64

[10] Small scale creation for solutions of the incompressible two-dimensional Euler equation [J].

Kiselev, Alexander ;

Sverak, Vladimir .

ANNALS OF MATHEMATICS, 2014, 180 (03) :1205-1220

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