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mathematics subject classification : 32c17, 53c21, 58d17 (2) 2
mathematics subject classification : 58d27, 58h15, 58d17, 53a30, 32g13, 58g05 (2) 2
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systems theory, control (2) 2
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Journal of Topology, ISSN 1753-8416, 03/2020, Volume 13, Issue 1, pp. 175 - 186
We use classical results in smoothing theory to extract information about the rational homotopy groups of the space of Riemannian metrics without conjugate... 
58D17 (primary) | 57R10 (secondary)
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 12/2019, Volume 58, Issue 6, pp. 1 - 7
We prove a $$C^{1,1}$$ C1,1 estimate for solutions of a class of fully nonlinear equations introduced by Chen–He. As an application, we prove the $$C^{1,1}$$... 
Primary: 58E10 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | 35J60 | Analysis | Theoretical, Mathematical and Computational Physics | 35J70 | Mathematics | Secondary: 58D17
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 9/2017, Volume 209, Issue 3, pp. 749 - 835
We study the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds. Hitchin used the fact that there... 
58J20 | 57R90 | 58D17 | 58D05 | 19K56 | 53C27 | Mathematics | 57R65 | 19D06 | 55R35 | 55S35 | 57R22 | 55P47 | Mathematics, general | HOMOTOPY TYPE | MATHEMATICS | THEOREM | SIMPLY CONNECTED MANIFOLDS | METRICS | CLASSIFICATION | INDEX | Theorems | Homotopy theory | Manifolds (mathematics) | Curvature
Journal Article
Journal of Topology, ISSN 1753-8416, 12/2019, Volume 12, Issue 4, pp. 1246 - 1265
We introduce an invariant of tuples of commuting diffeomorphisms on a 4‐manifold using families of Seiberg–Witten equations. This is a generalization of... 
58D17 (secondary) | 57R57 (primary) | ISOTOPY | MATHEMATICS | INVARIANTS
Journal Article
Science China Mathematics, ISSN 1674-7283, 8/2019, Volume 62, Issue 8, pp. 1511 - 1518
By taking a functional analytic point of view, we consider a family of distributions (continuous linear functionals on smooth functions), denoted by {μ t , t >... 
Brownian motion | law of iterated logarithm | compact manifold | 58D17 | 60B10 | Mathematics | Applications of Mathematics | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Osaka Journal of Mathematics, ISSN 0030-6126, 03/2013, Volume 50, Issue 1, pp. 31 - 51
In this paper, we study a connected non-parabolic, or transient, network compactified with the Kuramochi boundary, and show that the random walk converges... 
MATHEMATICS | CONVERGENCE | ENERGY | MAPS | GRAPHS | 58D17 | 53C21 | 58J50
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 2/2013, Volume 23, Issue 1, pp. 334 - 366
We study the geometry of the space of densities Dens(M), which is the quotient space Diff(M)/Diff μ (M) of the diffeomorphism group of a compact manifold M by... 
58D17 | 58D05 | geodesics | Riemannian metrics | 53C21 | Mathematics | Fisher–Rao metric | curvature | Hellinger distance | Analysis | Diffeomorphism groups | Euler–Arnold equations | integrable systems | Euler-Arnold equations | Fisher-Rao metric | MATHEMATICS | GEODESIC-FLOW | EQUATIONS | Naturvetenskap | Natural Sciences | Matematik
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 8/2018, Volume 197, Issue 4, pp. 1247 - 1268
We provide an algebraic description of the Teichmüller space and moduli space of flat metrics on a closed manifold or orbifold and study its boundary, which... 
Collapse | 57M60 | 58D17 | 58D27 | 53C24 | Teichmueller space | Mathematics | 32G15 | 53C15 | Gromov–Hausdorff convergence | 53C29 | 57R18 | Moduli space | Flat manifolds | Mathematics, general | 22E40 | Flat orbifolds | MATHEMATICS | MATHEMATICS, APPLIED | BIEBERBACH-GROUPS | SPACES | Gromov-Hausdorff convergence | CRYSTALLOGRAPHIC GROUPS | ESSAY
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2018, Volume 50, Issue 1, pp. 96 - 107
We show that in each dimension 4n+3, n⩾1, there exist infinite sequences of closed smooth simply connected manifolds M of pairwise distinct homotopy type for... 
53C20 | 53C30 | 58D17 | 58D27 (primary) | 57R55 (secondary) | 53C23 | 57R19 | BUNDLES | NEGATIVELY CURVED METRICS | RICCI CURVATURE | MATHEMATICS | SOULS | POSITIVE SCALAR CURVATURE | HYPERBOLIC MANIFOLD | SPECTRAL ASYMMETRY | LOOP-SPACES | RIEMANNIAN GEOMETRY | Mathematics - Differential Geometry
Journal Article
Science China Mathematics, ISSN 1674-7283, 4/2017, Volume 60, Issue 4, pp. 569 - 580
We prove that for all n = 4k − 2 and k ≥ 2 there exists a closed smooth complex hyperbolic manifold M with real dimension n having non-trivial π 1(T <0(M)). T... 
53C20 | 58D17 | 58D27 | 53C55 | Mathematics | Applications of Mathematics | negative curvature | space of Riemannian metrics | 57R19 | complex hyperbolic space | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 08/2016, Volume 39, Issue 12, pp. 3163 - 3172
In this research article, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza–Klein black hole space‐time in a Riemannian... 
optimal system | 58D17 | Noether theorem | 58J70 | Lie point symmetry | space‐time metric | subclass 76M60 | space-time metric | MATHEMATICS, APPLIED | CONSERVATION-LAWS | GEODESIC EQUATIONS | Conservation laws | Black holes | Spacetime | Mathematical analysis | Geodesy | Lie groups | Transformations | Invariants | Optimization | Symmetry
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 03/2013, Volume 30, Issue 2, pp. 251 - 274
We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L2 metric. Among these we characterize a... 
MATHEMATICS, APPLIED | CURVES | MANIFOLD | Mathematics - Differential Geometry
Journal Article
Differential Geometry and its Applications, ISSN 0926-2245, 04/2015, Volume 39, pp. 166 - 183
We study metrics on shape space of immersions that have a particularly simple horizontal bundle. More specifically, we consider reparametrization invariant... 
Shape space | Curve matching | Riemannian shape analysis | Infinite dimensional geometry | Sobolev type metric | Reparametrization group | RIEMANNIAN METRICS | MATHEMATICS | SOBOLEV METRICS | MATHEMATICS, APPLIED | HYPERSURFACES | CURVES | Mathematics - Differential Geometry
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 10/2016, Volume 11, Issue 5, pp. 1335 - 1343
These notes present and survey results about spaces and moduli spaces of complete Riemannian metrics with curvature bounds on open and closed manifolds, here... 
moduli spaces | 53C20 | 58D17 | 58D27 | positive Ricci curvature | 53C23 | Riemannian metrics | Mathematics, general | Mathematics | positive scalar curvature | 57R19 | sectional curvature | MATHEMATICS | BUNDLES | INVARIANTS | SOULS | HYPERBOLIC MANIFOLD | NEGATIVELY CURVED METRICS | Studies | Topological manifolds | Mathematical analysis | Manifolds | Curvature | Disengaging
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 12/2010, Volume 20, Issue 6, pp. 1397 - 1430
In the first part of the paper we introduce the theory of bundles with negatively curved fibers. For a space X there is a forgetful map F X between bundle... 
53C20 | 58D17 | 58D27 | 57N37 | Analysis | pseudoisotopies | Mathematics | bundle theories | negative curvature | 57R19 | Space of Riemannian metrics | MATHEMATICS | MAPS | STABILITY | MANIFOLDS
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2/2013, Volume 273, Issue 1, pp. 55 - 93
Given a fixed closed manifold M, we exhibit an explicit formula for the distance function of the canonical L 2 Riemannian metric on the manifold of all smooth... 
Manifold of metrics | Secondary 58B20 | L 2 metric | Nonpositive curvature | Completion | CAT | 51F99 | Mathematics, general | Mathematics | Primary 58D17 | metric | MATHEMATICS | L-2 metric | HARMONIC MAPS | SPACES | GEOMETRY
Journal Article
Journal of Dynamical Systems and Geometric Theories, ISSN 1726-037X, 07/2015, Volume 13, Issue 2, pp. 163 - 178
In this paper we have introduced the notion of almost conformai gradient shrinking Ricci soliton and established some curvature identities for almost conformai... 
Ricci soliton | 58D17 | curvature operator | 53C44 | Ricci flow | conformai Ricci flow | almost Ricci soliton | gradient conformai Ricci soliton | 35K65
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 11/2010, Volume 39, Issue 3, pp. 533 - 545
Journal Article
Regular and Chaotic Dynamics, ISSN 1560-3547, 7/2015, Volume 20, Issue 4, pp. 463 - 475
Journal Article
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