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2003, ISBN 9789812386878, viii, 262
Book
Potential Analysis, ISSN 0926-2601, 11/2018, Volume 49, Issue 4, pp. 555 - 581
We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat... 
Geometry | 53B21 | Submanifold | 58J65 | Potential Theory | Functional Analysis | Heat kernel | Probability Theory and Stochastic Processes | Mathematics | Local time | Brownian bridge | 60J55 | COMPARISON THEOREM | DISTANCE | DIFFUSION-PROCESSES | EQUATIONS | MEAN-CURVATURE FLOW | DIRICHLET SPACES | TIME ASYMPTOTICS | COMPACT RIEMANNIAN MANIFOLD | MATHEMATICS | FUNDAMENTAL SOLUTION | Employee motivation | Analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 2, pp. 1308 - 1326
In this paper we present some linear algebra behind quadratic parts of quadratically flat complex points of codimension two real submanifold in a complex... 
Complex points | Simultaneous reduction | CR manifolds | Normal forms | MATHEMATICS, APPLIED | C-N | LOCAL HULL | REAL SURFACES | HOLOMORPHY | CONSIMILARITY | CANONICAL FORM | MATHEMATICS | LEVI-FLAT HYPERSURFACES | NONSINGULAR PENCIL | HERMITIAN MATRICES | TRANSFORMATIONS | Mathematics - Complex Variables
Journal Article
Journal of Knot Theory and Its Ramifications, ISSN 0218-2165, 09/2019, Volume 28, Issue 10, p. 1950068
We first prove the following: Let p ≥ 2 and p ∈ ℕ . Let K and J be closed, oriented, ( 2 p + 1 ) -dimensional ( p − 1 ) -connected, simple submanifolds of S 2... 
local moves on high-dimensional knots | INVARIANTS | pass-moves on 1-links | CLASSIFICATION | RIBBON-MOVES | crossing changes on 1-links | Brieskorn submanifolds | MATHEMATICS | local moves on 1-knots | Seifert hypersurfaces | Seifert matrices | Brieskorn manifolds | pass-moves on high-dimensional links | Products of knots | twist-moves on high-dimensional links
Journal Article
International Journal of Mathematics, ISSN 0129-167X, 04/2013, Volume 24, Issue 4, pp. 1350028 - 1350026
Chen famously conjectured that every submanifold of Euclidean space with harmonic mean curvature vector is minimal. In this note, we establish a much more... 
higher order partial differential equations | global differential geometry | geometric analysis | higher order | Local differential geometry | MATHEMATICS | Manifolds | Harmonics | Infinity | Mathematical analysis | Mathematics | Cases (containers) | Vectors (mathematics) | Curvature | Mathematics - Differential Geometry
Journal Article
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, ISSN 0022-3239, 07/2019, Volume 182, Issue 1, pp. 189 - 210
The property of continuous differentiability with Lipschitz derivative of the square distance function is known to be a characterization of prox-regular sets.... 
Metric projection | Diffeomorphism | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Distance function | Local uniform continuity | Prox-regular set | Hilbert space | Submanifolds | Manifolds (mathematics) | Smoothness
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 275, Issue 1, pp. 115 - 165
Real-analytic Levi-flat codimension-two CR singular submanifolds are a natural generalization to C-m, m > 2, of Bishop surfaces in C-2. Such submanifolds, for... 
Bishop surface | CR singular | Mixed-holomorphic equations | Codimension two | Levi-flat | Normal form | LOCAL HULL | codimension two | HOLOMORPHY | COMPLEX TANGENTS | SPACE | MATHEMATICS | mixed-holomorphic equations | HYPERSURFACES | MANIFOLDS | BOUNDARY | DOMAINS | TRANSFORMATIONS | REAL ANALYTIC SURFACES | Mathematics - Complex Variables
Journal Article
JOURNAL OF DIFFERENTIAL GEOMETRY, ISSN 0022-040X, 05/2019, Volume 112, Issue 1, pp. 121 - 198
We study germs of real analytic n-dimensional submanifold of C-n that has a complex tangent space of maximal dimension at a CR singularity. Under some... 
divergent normal forms | MATHEMATICS | Local analytic geometry | CR singularity | small divisors | integrability | NORMAL FORMS | reversible mapping | Complex Variables | Dynamical Systems | Mathematics
Journal Article
JOURNAL OF GEOMETRY AND PHYSICS, ISSN 0393-0440, 04/2018, Volume 127, pp. 1 - 13
We study Lagrangian submanifolds of the nearly Kahler S-3 x S-3 with respect to their so called angle functions. We show that if all angle functions are... 
Immersions | MATHEMATICS | Nearly Kahler manifolds | 6-SPHERE | Lagrangian submanifolds | MANIFOLDS | PHYSICS, MATHEMATICAL | Local submanifolds
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 11/2016, Volume 206, Issue 2, pp. 293 - 377
We study a germ of real analytic n-dimensional submanifold of $${\mathbf {C}}^n$$ C n that has a complex tangent space of maximal dimension at a CR... 
37G05 | Mathematics, general | Mathematics | 32V40 | 37F50 | 32S05 | DIFFEOMORPHISMS | MATHEMATICS | ANALYTIC SURFACES | LOCAL HULL | STABILITY | MANIFOLDS | HOLOMORPHY | NORMALIZATION | Equivalence | Manifolds (mathematics) | Dimensional analysis | Tangents | Singularities | Mathematical analysis | Texts | Formulas (mathematics) | Complex Variables | Dynamical Systems
Journal Article
Journal of Geometric Analysis, ISSN 1050-6926, 07/2017, Volume 27, Issue 3, pp. 2453 - 2471
Let M subset of Cn+1, n >= 2, be a real codimension two CR singular real analytic submanifold that is nondegenerate and holomorphically flat. We prove that... 
Hartogs–Bochner | Levi-flat Plateau problem | Extension of CR functions | CR singularity | SPACE | MATHEMATICS | Hartogs-Bochner | LOCAL HULL | SURFACE | NORMAL FORMS | MANIFOLDS | HOLOMORPHY | Mathematics - Complex Variables
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 04/2018, Volume 127, pp. 1 - 13
We study Lagrangian submanifolds of the nearly Kähler with respect to their so called angle functions. We show that if all angle functions are constant, then... 
Immersions | Nearly Kähler manifolds | Lagrangian submanifolds | Local submanifolds
Journal Article
Advances in Mathematics, ISSN 0001-8708, 2007, Volume 209, Issue 2, pp. 460 - 525
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 6, pp. 995 - 1004
In this survey article, we present some known results and also propose some open questions related to the analytic and geometric aspects of Bishop submanifolds... 
Levi-flat hypersurfaces | MATHEMATICS, APPLIED | Bishop invariants | LOCAL HULL | holomorphic disks | HOLOMORPHY | COMPLEX TANGENTS | CR singular points | SPACE | MATHEMATICS | local hull of holomorphy | NORMAL FORMS | BOUNDARY | hyperbolic structure | TRANSFORMATIONS | SURFACES
Journal Article
Potential Analysis, ISSN 0926-2601, 10/2016, Volume 45, Issue 3, pp. 485 - 508
This is a study of the distance between a Brownian motion and a submanifold of a complete Riemannian manifold. It contains a variety of results, including an... 
53B21 | Submanifold | Tube | 58J65 | Probability Theory and Stochastic Processes | Mathematics | Local time | Geometry | Brownian motion | Potential Theory | Functional Analysis | Distance | 60J55 | MATHEMATICS | RADIAL PART | LOGARITHMIC SOBOLEV INEQUALITIES | CUT LOCUS | COMPLETE RIEMANNIAN MANIFOLD
Journal Article
Finite Fields and Their Applications, ISSN 1071-5797, 2011, Volume 17, Issue 4, pp. 303 - 316
In this article, we consider the estimation of exponential sums along the points of the reduction mod of a -adic analytic submanifold of . More precisely, we... 
Congruences in many variables | Exponential sums mod [formula omitted] | p-Adic manifolds | Poincaré series | Igusa local zeta function | Exponential sums mod | VARIETY | FIELDS | MATHEMATICS, APPLIED | LOCAL ZETA-FUNCTION | NEWTON POLYHEDRA | Poincare series | MATHEMATICS | MAPPINGS | Exponential sums mod p(m) | POINTS
Journal Article
Siberian Mathematical Journal, ISSN 0037-4466, 11/2015, Volume 56, Issue 6, pp. 996 - 1008
We construct some new local diffeomorphism that enables us to study submanifolds of matrices. Using the diffeomorphism, we define the parametrization of the... 
Mathematics, general | Mathematics | parametrization | local diffeomorphism | submanifold of matrices | Jordan form
Journal Article
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