Paper extends option spanning results for non-integrable assets.
problem Spanning power of options in non-integrable assets.
method Unified results for Lp-models and applied to pricing problem. result Option prices can be extended to all contingent claims.
Solves Monge-Ampère on non-integrable manifolds.
problem Existence and uniqueness of solutions to Monge-Ampère equation on non-integrable almost complex manifolds.
method Existence and uniqueness proved using the Monge-Ampère equation.
result Existence and uniqueness of solutions proved.
Study non-integrable distributions with various affine connections.
problem Characterize non-integrable distributions in Riemannian manifolds with different connections.
method Obtain Gauss, Codazzi, and Ricci equations for non-integrable distributions with semi-symmetric metric, non-metric, and statistical connections.
result Find new examples of Einstein and distributions with constant scalar curvature.
The paper proves a theorem for non-integrable projective distributions of degree one.
problem Classifying non-integrable projective distributions of degree one.
method Proving a singular Darboux type theorem for homogeneous polynomial closed 2-forms of degree one.
result Classification of non-integrable codimension one distributions of degree one.
The study examines stability of Hamiltonian Poisson integrators on both integrable and non-integrable systems.
problem Investigating stability properties of Hamiltonian Poisson integrators.
method Examples of Lotka-Volterra dynamics and numerical investigations of a non-integrable system are used.
result The existence of a modified Hamiltonian is crucial for the stability of Hamiltonian Poisson integrators.
Study h-principles for non-integrable distributions on manifolds.
problem Existence and classification of maximally non-integrable distributions of derived length one.
method Introduced formal structures and used h-principles to discuss existence and classification.
result Discussed existence and classification of maximally non-integrable distributions of derived length one.
Local coordinates for non-integrable Lie algebroids constructed.
problem Constructing local coordinates for non-integrable Lie algebroids.
method Reformulating bi-submersion algebraically and proving their existence for the Weinstein groupoid.
result Existence of C∗-algebra attached to every Lie algebroid. Detecting closed essential surfaces in 3-manifolds is challenging.
problem Detecting closed essential surfaces in 3-manifolds using ideal points of character varieties or algebraic non-integral representations.
method Using Chesebro's module-theoretic interpretation of Culler-Shalen theory, constructing examples of 3-manifolds with no algebraic non-integral representations.
result Construction of an infinite family of closed hyperbolic Haken 3-manifolds with no algebraic non-integral representations into PSL(2, C).
We study the classification of singularities of holomorphic foliations and non-integrable one-forms under the hypothesis of transversality with real hypersurfaces.
We show that on any hyperbolic knot in S3 there is at most one non-integral Dehn surgery which yields a manifold containing an incompressible torus.
Study Liouville-type results for non-integrable almost complex manifolds.
problem Establish Liouville-type results for almost complex manifolds.
method Combine techniques from Xiaokui Yang, Valentino Tosatti, and others. Discuss key differences and introduce tools.
result Present proof of main theorem.
Classifies non-integrable distributions with simple infinite-dimensional Lie superalgebras of symmetries.
problem Classifying non-integrable distributions with specific Lie superalgebras.
method Classification based on locality assumptions and W-grading.
result 15 series and 7 exceptional Lie superalgebras identified over C, and analogs over K of characteristic p>0. We study the types of non-integrable G-structures on Riemannian manifolds. In particular, geometric types admitting a connection with totally skew-symmetric torsion are characterized. 8-dimensional manifolds equipped with a $\Spin(7)$-structure play a special role. Any geometry of that type admits a unique c…
Study non-integrated defect relations for complete minimal surfaces in higher dimensions.
problem Understanding defect relations for Gauss maps of minimal surfaces.
method Extending previous work to higher dimensions, focusing on surfaces with finite total curvature.
result Non-integrated defect relations for Gauss maps of complete minimal surfaces in Rm are established. Non-Euclidean number rings have non-integral Steinberg modules.
problem Characterizing when Steinberg modules are generated by integral elements.
method Analyzing special linear groups over non-Euclidean imaginary number rings.
result Steinberg modules are not generated by integral elements in non-Euclidean rings.
The paper explores cohomologies on almost complex manifolds and their applications.
problem Distinguishing and understanding cohomologies on non-integrable almost complex structures.
method Defined and studied cohomologies HN∙(M) and HJ∙(M) using Nijenhuis-Lie derivations. result The J-cohomology encodes whether an almost complex structure satisfies the dLJ-lemma. This paper addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface xyz=1. We prove this is the case using the Morales-Ramis theorem and Kovacic algorithm. We also consider some consequences and extensions of this result.
Study shows non-integrability of magnetic billiards on curved surfaces.
problem Non-existence of polynomial integrals for magnetic billiards.
method Examined billiard motion on constant curvature surfaces with magnetic fields.
result For most magnetic field values, billiard motion lacks polynomial integrals.
Study geodesic flow on graph-related nilmanifolds, finding integrable and non-integrable cases.
problem Understanding geodesic flow on specific geometric structures.
method Construction of first integrals to show complete integrability.
result Examples of integrable and non-integrable geodesic flows.
This paper concerns the problem of existence of taut foliations among 3-manifolds. Since the contribution of David Gabai, we know that closed 3-manifolds with non-trivial second homology group admit a taut foliations. The essential part of this paper focuses on Seifert fibered homology 3-spheres. The result is quite di…
We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the Chern-Moser normalization into pure intrinsic setting, whereas the other directly extends the (extrinsic) Chern-Moser normal form by allowing non-C…
Study shows almost complex structures with certain tensor properties are prevalent.
problem Characterizing almost complex structures with specific tensor properties.
method Analyzes the space of almost complex structures on compact manifolds.
result The space of almost complex structures with rank at least k Nijenhuis tensor is either empty or dense in each component.
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics--in particular superstring theory--where these naturally appear. Connections with skew-symmetric torsion…
Study shows magnetic billiards are algebraically non-integrable in most cases.
problem Non-integrability of magnetic billiards in convex domains.
method Analyzing polynomial integrals of motion in magnetic billiard flows.
result Magnetic billiards are algebraically non-integrable for most smooth boundary curves.
Enhances method for constructing integral manifolds of non-integrable Pfaffian systems.
problem Constructing maximal integral manifolds for non-integrable Pfaffian systems.
method Recurrent geometrical method developed by Élie Cartan and von Weber.
result Enhanced Jordan-Hölder integration procedure for constructing local maximal integral manifolds.
We define invariants for colored oriented spatial graphs by generalizing CM invariants, which were defined via non-integral highest weight representations of Uq(sl2). We apply the same method to define Yokota's invariants, and we call these invariants Yokota type invariants. Then we propose a volume conjecture of t…
Study geodesic rays in Teichmüller space and their limits in Thurston's boundary.
problem Characterize limits of geodesic rays in Thurston's boundary of Teichmüller space.
method Analyze geodesic rays in T(D) and their limits in PMLbdd(D). result Geodesic rays in T(D) can limit to projective measured laminations with non-homotopic leaves. Study on sub-Riemannian structures in low dimensions, proving non-integrability in some cases.
problem Integrability of rank 2 sub-Riemannian structures on low-dimensional manifolds.
method Analysis of symmetry and polynomial integrals in momenta for geodesic flows.
result Some rank 2 sub-Riemannian structures in 6, 7, and 8 dimensions are non-integrable.
The paper explores geometric properties of non-integrable distributions and their applications.
problem Characterizing and understanding non-integrable distributions in Riemannian manifolds.
method Analyzes the intrinsic connection and Levi-Civita connection on Riemannian manifolds, comparing their curvature and second fundamental form.
result Develops a new tool (second fundamental form) to characterize involutive and totally geodesic distributions.
Our goal here is to give a simple proof of the non integrable version of Brody's characterisation theorem.
The chaotic geodesic flow on a jet space is non-integrable.
problem Non-integrability of the sub-Riemannian geodesic flow on J2(R2,R). method Analysis of the Hamiltonian geodesic flow on the metabelian Carnot group structure of J2(R2,R). result The reduced Hamiltonian Hμ is non-integrable by meromorphic functions for some values of μ. The paper examines complex and para-complex structures on pseudo-Riemannian spheres.
problem Exploring non-integrable Cayley structures on pseudo-Riemannian spheres.
method Study of Cayley structures on six-dimensional pseudo-Riemannian spheres.
result Existence of complex and para-complex structures on pseudospheres.
New method shows trapped surfaces form in geodesic foliation.
problem Formation of trapped surfaces in Einstein vacuum equation.
method Geodesic foliation, non-integrable PT frame.
result Trapped surfaces form for Einstein vacuum equation.
Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.
problem Maximally non-integrable almost complex structures and their cohomological properties.
method h-principle and topological invariants characterization.
result Existence of almost complex structures with maximal Nijenhuis tensor rank on parallelizable and certain manifolds.
Characterizes actions of stacky Lie groupoids on differentiable stacks.
problem Understanding actions of stacky Lie groupoids on differentiable stacks.
method Characterization of principal actions of stacky Lie groupoids.
result Principal actions of stacky Lie groupoids yield differentiable stack quotients as principal bundles.
A contact manifold is a manifold equipped with a distribution of codimension one that satisfies a `maximal non-integrability' condition. A standard example of a contact structure is a strictly pseudoconvex CR manifold, and operators of analytic interest are the tangential Cauchy-Riemann operator and the Szego projector…
We show that a 7-dimensional non-compact Ricci-flat Riemannian manifold with Riemannian holonomy G_2 can admit non-integrable G_2 structures of type R + S^2_0(R^7) + R^7 in the sense of Fernández and Gray. This relies on the construction of some G_2 solvmanifolds, whose Levi-Civita connection is known to give a paralle…
A complex structure on a subset of S^6 cannot be extended to a global integrable structure.
problem Non-integrability of complex structures on subsets of S^6.
method Proving the non-integrability of extensions of a specific complex structure on a subset of S^6.
result It is impossible to deform a non-integrable structure to an integrable one on S^6 while fixing it on a subset.
Study G2-metrics from non-integrable special Lagrangian fibrations.
problem Understanding G2-metrics from non-integrable special Lagrangian fibrations. method Decompose SU(3)-structures into solder 1-forms, connection 1-forms, and equivariant matrix-valued functions. result Describe regular parts of G2-manifolds with Lagrangian-type actions. The basic class of the non-integrable almost complex manifolds with Norden metric is considered. Its curvature properties are studied. The isotropic Kaehler type of investigated manifolds is introduced and characterized geometrically.
New research shows that many slopes are characterizing for satellite knots.
problem Characterizing slopes for satellite knots.
method Detailed examination of the JSJ decomposition of a surgery along a knot, combined with other authors' constraints on surgery slopes.
result Many non-integral slopes are characterizing for composite knots.
Study minimal Lagrangian submanifolds of complex hyperquadric.
problem Classify minimal Lagrangian submanifolds of complex hyperquadric.
method Use non-integrable almost product structures and local angle functions.
result Classify minimal Lagrangian submanifolds with constant sectional curvatures and those with coinciding local angle functions.
The paper explores Kodaira dimension on almost complex manifolds.
problem Understanding Kodaira dimension on non-integrable almost complex manifolds.
method Generalization of Kodaira dimension to almost complex manifolds and study of its behavior under deformations.
result Kodaira dimension is invariant under holomorphic deformations for smooth projective manifolds but not for non-projective manifolds.
The paper explores Hodge decomposition and Hard Lefschetz Condition on almost Kähler manifolds.
problem Analyzing harmonic forms and Hodge decomposition on almost Kähler manifolds.
method Using Hodge decomposition and the Hard Lefschetz Condition to study almost Kähler manifolds.
result The spaces of harmonic forms have the Hodge decomposition and the Hard Lefschetz Condition is satisfied.
New pseudo-Kähler Einstein spaces found with special almost complex structures.
problem Identifying new pseudo-Kähler Einstein spaces with special almost complex structures.
method Examining 4-symmetric symplectic spaces with compatible almost complex structures.
result Found pseudo-Kähler Einstein spaces with an integrable and non-integrable pair of compatible almost complex structures.
Infinite knots have non-integer trace values.
problem Finding knots with non-integer trace values.
method Proved existence of infinitely many non-homeomorphic hyperbolic knot complements with specific trace properties.
result Infinitely many non-homeomorphic hyperbolic knot complements with non-integer trace values.
We study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to some (pseudo)-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provi…
We prove that the Calabi-Yau equation can be solved on the Kodaira-Thurston manifold for all given T2-invariant volume forms. This provides support for Donaldson's conjecture that Yau's theorem has an extension to symplectic four-manifolds with compatible but non-integrable almost complex structures.