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)

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

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

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

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

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

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

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

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

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

53C20 | 58D17 | 58D27 | 53C55 | Mathematics | Applications of Mathematics | negative curvature | space of Riemannian metrics | 57R19 | complex hyperbolic space | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 3/2015, Volume 61, Issue 3, pp. 553 - 573

Inexact proximal point methods are extended to find singular points for multivalued vector fields on Hadamard manifolds. Convergence criteria are established...

Operations Research/Decision Theory | Inexact proximal point algorithms | Hadamard manifolds | Mathematics | Monotone vector fields | Primary 49J40 | Secondary 58D17 | Computer Science, general | Optimization | Real Functions | Convergence analysis | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | GAMMA-CONDITION | UNIQUENESS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVARIANT ALPHA-THEORY | BANACH-SPACES | OPERATORS | RIEMANNIAN-MANIFOLDS | Analysis | Algorithms | Studies | Optimization algorithms | Linear algebra | Manifolds | Inequalities | Texts | Lithium | Fields (mathematics) | Convergence

Operations Research/Decision Theory | Inexact proximal point algorithms | Hadamard manifolds | Mathematics | Monotone vector fields | Primary 49J40 | Secondary 58D17 | Computer Science, general | Optimization | Real Functions | Convergence analysis | NONSMOOTH ANALYSIS | MATHEMATICS, APPLIED | MONOTONE VECTOR-FIELDS | GAMMA-CONDITION | UNIQUENESS | VARIATIONAL-INEQUALITIES | NEWTONS METHOD | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVARIANT ALPHA-THEORY | BANACH-SPACES | OPERATORS | RIEMANNIAN-MANIFOLDS | Analysis | Algorithms | Studies | Optimization algorithms | Linear algebra | Manifolds | Inequalities | Texts | Lithium | Fields (mathematics) | Convergence

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

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

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

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

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

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

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

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

We prove that the L 2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space...

Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | 58D17 (Primary) | 58B20 (Secondary) | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | DIFFEOMORPHISM GROUP | SPACES | Manifolds | Mapping | Metric space | Partial differential equations | Mathematical analysis | Calculus of variations

Calculus of Variations and Optimal Control; Optimization | Systems Theory, Control | Theoretical, Mathematical and Computational Physics | Analysis | 58D17 (Primary) | 58B20 (Secondary) | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | DIFFEOMORPHISM GROUP | SPACES | Manifolds | Mapping | Metric space | Partial differential equations | Mathematical analysis | Calculus of variations

Journal Article

Regular and Chaotic Dynamics, ISSN 1560-3547, 7/2015, Volume 20, Issue 4, pp. 463 - 475

The second-order integrable Killing tensor with simple eigenvalues and vanishing Haantjes torsion is the key ingredient in construction of Liouville integrable...

58D17 | 70E40 | Mathematics | Dynamical Systems and Ergodic Theory | Killing tensors | separation of variables | 53A60 | integrable systems | STACKEL | MATHEMATICS, APPLIED | MECHANICS | CANONICAL-TRANSFORMATIONS | EXTENDED PHASE-SPACE | HAMILTON-JACOBI EQUATION | PHYSICS, MATHEMATICAL | VARIABLE SEPARATION | RIEMANNIAN-MANIFOLDS | Euclidean geometry | Mathematical research | Geometry, Plane | Research | Equations of motion | Tensors (Mathematics) | Geometry, Solid

58D17 | 70E40 | Mathematics | Dynamical Systems and Ergodic Theory | Killing tensors | separation of variables | 53A60 | integrable systems | STACKEL | MATHEMATICS, APPLIED | MECHANICS | CANONICAL-TRANSFORMATIONS | EXTENDED PHASE-SPACE | HAMILTON-JACOBI EQUATION | PHYSICS, MATHEMATICAL | VARIABLE SEPARATION | RIEMANNIAN-MANIFOLDS | Euclidean geometry | Mathematical research | Geometry, Plane | Research | Equations of motion | Tensors (Mathematics) | Geometry, Solid

Journal Article

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