The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.
problem Exploring new types of manifolds in general relativity.
method Generalization of existing manifolds and construction of specific examples.
result Existence and properties of extended quasi-Einstein manifolds with solitons.
No Einstein metrics found on extended graph 4-manifolds.
problem Finding Einstein metrics on extended graph 4-manifolds.
method Defined and analyzed extended graph 4-manifolds as per [FLS15].
result Extended graph 4-manifolds do not support Einstein metrics.
The paper studies lifts of complex structures on a manifold.
problem Understanding higher-order lifts of extended almost complex structures.
method Proved theorems on Nijenhuis tensor and introduced a new tensor field.
result Basic results on almost analytic complex vectors are investigated.
Extends index theory results to manifolds with boundaries.
problem Applying index theory to manifolds with boundaries.
method Extends results of Llarull and Goette-Semmelmann.
result Results extended to manifolds with boundaries.
Proves theorem for Riemannian manifolds, extending previous work.
problem Proving Quantitative Fatou Theorem on Riemannian manifolds.
method Extending ε-approximation lemma to manifold setting.
result Proves Quantitative Fatou Theorem for Lipschitz domains on Riemannian manifolds.
Improved Kalman filter for Stiefel manifold measurements.
problem Improving accuracy in measurements on Stiefel manifolds.
method Generalization of extended Kalman filter for Stiefel manifold-valued measurements.
result Significant improvement over raw measurements.
Extends Einstein-Hilbert functional definition for stable manifolds.
problem Stability of Einstein manifolds on Riemannian manifolds.
method Second variation of generalized Einstein-Hilbert functional.
result Properties of stable Einstein manifolds presented.
Extends K-cowaist inequality to manifolds with boundary.
problem Applying K-cowaist inequality to manifolds with boundary.
method Extended K-cowaist inequality for generalized Dirac operators on manifolds with boundary.
result New applications of K-cowaist inequality to manifolds with boundary.
New findings on Frobenius structures on Kodaira manifolds.
problem Understanding Frobenius structures on Kodaira manifolds.
method Extended deformation theory and Frobenius structures.
result Frobenius structure on Kodaira manifolds is trivial on degree-2 component.
Study on embeddings of surfaces in 4-manifolds and their mapping classes.
problem Characterizing and understanding embeddings of surfaces in 4-manifolds and their mapping classes.
method Analyzing smooth proper embeddings and mapping classes induced by diffeomorphisms of 4-manifolds.
result Most surfaces do not admit flexible embeddings in 4-manifolds with specific homology types.
Extends Kodaira Spencer to higher-dimensional Calabi-Yau manifolds.
problem No specific problem stated; extension of functional.
method Extension to Calabi-Yau manifolds of arbitrary dimension.
result Extension of the Kodaira Spencer functional.
Extends Tian theorem to Vaisman manifolds for approximations.
problem Approximating Vaisman metrics by immersions/embeddings.
method Study Vaisman metrics on compact manifolds.
result Extend Tian's theorem to Vaisman manifolds.
Extended Einstein manifolds reveal new symmetries.
problem Understanding symmetries of Einstein manifolds.
method Constructed a line bundle from projective compactification and identified its automorphisms as asymptotic symmetries.
result Asymptotic symmetries identified on extended boundaries of Einstein manifolds.
Extends Llarull's theorem to noncompact manifolds with boundary.
problem Generalizing Llarull's theorem to noncompact manifolds with boundary.
method Extends previous results to include compact boundaries.
result Generalized theorem to noncompact manifolds with compact boundaries.
Finite groups act freely on surfaces but not on 3-manifolds.
problem Understanding finite group actions on surfaces and 3-manifolds.
method Analyzing homeomorphisms of surfaces and 3-manifolds.
result Finite groups can act freely on surfaces but not on handlebodies.
Extends Seifert algorithm to 3-manifolds via surgery.
problem Construct Seifert surfaces in arbitrary 3-manifolds.
method Uses surgery on framed links in S^3 to extend classical algorithm.
result Explicit construction of Seifert surfaces in 3-manifolds.
Extends a result on manifolds with specific curvature properties.
problem Extending a result on manifolds with nonnegative Bakry-Émery Ricci curvature.
method Extends a recent result by S. Brendle to manifolds with densities and nonnegative Bakry-Émery Ricci curvature.
result Extends a result on manifolds with specific curvature properties.
We define the category of manifolds with extended tangent bundles, we study their symmetries and we consider the analogue of equivariant cohomology for actions of Lie groups in this category. We show that when the action preserves the splitting of the extended tangent bundle, our definition of extended equivariant coho…
Extended recurrent pseudo-Riemannian manifolds were introduced by Mileva Prvanovic'. We reconsider her work in the light of recent results and show that the manifold is conformally flat, and it is a space of quasi-constant curvature. We also show that an extended recurrent Lorentzian manifold, with time-like associated…
Extends rigidity results to non-homogeneous manifolds.
problem Measure and topological rigidity in dynamical systems.
method From homogeneous to general manifolds.
result Measure and topological rigidity results extended.
Extended equivariant BV formalism to manifolds with boundaries.
problem Handling manifolds with boundaries in equivariant BV formalism.
method Extension of AKSZ theories to manifolds with boundaries.
result Successfully applied to manifolds with boundaries.
Finite group actions on surfaces extend to 3-manifolds.
problem Classifying extendable periodic automorphisms of surfaces.
method Using fixed embeddings and 1-dominated 3-manifolds.
result All periodic automorphisms of closed surfaces extend to 3-spheres.
Extends 4D cornered skein theory to surfaces, proving gluing formulas.
problem Formulating gluing formulas for 4-manifolds with corners and boundaries.
method Develops a categorical framework and introduces bicategories for closed surfaces.
result Proves gluing formulas for categories associated with 3-manifolds with boundary.
Extends geometric structures to manifolds with new operators.
problem No specific problem stated; extending geometric structures.
method Defines new gradient and Laplace operators on manifolds with geometric structures.
result Provides properties of the new operators.
For a particular class of pseudo manifolds, we show that the intersection cohomology groups for any perversity may be naturally represented by extended weighted L2 harmonic forms for a complete metric on the regular stratum with respect to some weight determined by the perversity. Extended weighted L2 harmonic fo…
The study extends group actions from surfaces to 3-manifolds using G-cobordisms.
problem When a finite group action on a surface extends to a 3-manifold.
method Using Schur multiplier and G-cobordisms, the study examines principal actions. result Affirmative extension for abelian, dihedral, symmetric, and alternating groups.
The first author in recent work with D. Gay developed the notion of a Morse structure on an open book as a tool for studying closed contact 3-manifolds. We extend the notion of Morse structure to extendable partial open books in order to study contact 3-manifolds with convex boundary.
Extends parabolic study to flat hyperkähler manifolds.
problem Study problems in hyperhermitian geometry.
method Extends elliptic approach to parabolic setting.
result Solves problems in hyperhermitian geometry.
Abstract: Study Hamiltonian systems on almost cosymplectic manifolds, extending contact Hamiltonian systems.
problem Extend Hamiltonian systems to almost cosymplectic manifolds.
method Determine Hamiltonian vector field on odd-dimensional almost cosymplectic manifolds.
result Extend equations of motion to generalized transitive almost cosymplectic structures.
Study extends compactness theorems to weighted manifolds with integral curvature bounds.
problem Estimating diameter of weighted manifolds under curvature constraints.
method Extended Sprouse's compactness theorems to weighted manifolds with integral curvature bounds. Used ε-range to handle specific cases. Extended segment inequality to weighted manifolds.
result Proved theorems for weighted manifolds with effective dimension ≤ 1 and ≥ dimension.
Extends differential geometry concepts to manifolds with super tangent bundles.
problem No specific problem stated; extending differential geometry to super tangent bundles.
method Introduces super tangent bundle and extends differential geometry concepts.
result Basic notions of differential geometry extended to manifolds with super tangent bundles.
Extends BCOV invariant to pairs of Calabi-Yau manifolds and pluricanonical divisors.
problem Extend BCOV invariant to new geometric pairs.
method Extend BCOV invariant to pairs (X,D), study blow-up behavior. result Results imply birational Calabi-Yau manifolds have the same BCOV invariant.
Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.
problem Applying Kobayashi-Hitchin correspondence to non-Kähler manifolds.
method Continuity method for vortex equation, Kobayashi-Hitchin correspondence for holomorphic pairs.
result Proved solvability of vortex equation on holomorphic vector bundles over compact Hermitian manifolds.
New proof shows 4-manifolds can't support complex structures.
problem Proving 4-manifolds can't support complex structures.
method New proof of complex structure non-existence for real-hyperbolic 4-manifolds.
result Extended graph 4-manifolds with positive Euler characteristic cannot support a complex structure.
The paper extends knot theory to 4-manifolds, defining new genera and obstructions.
problem Understanding embeddings of 3-manifolds into 4-manifolds with specific properties.
method New L2-signature obstructions and extensions of knot genera. result Existence of knots with arbitrarily large generalized superslice genera and double stabilizing numbers.
Extends ASD connection existence to 4-manifolds with cylindrical ends.
problem Existence of ASD connections on 4-manifolds with specific ends.
method Extends gluing theorems to cylindrical ends, using mASD connections.
result Establishes existence of ASD connections on 4-manifolds with cylindrical ends.
The paper constructs gluing maps for harmonic maps between Riemannian manifolds.
problem Constructing harmonic maps between Riemannian manifolds.
method Gluing construction of extended harmonic maps.
result Construction of gluing maps for harmonic maps under specific conditions.
Extends integrability to cosymplectic manifolds.
problem Integrability of Hamiltonian systems on cosymplectic manifolds.
method Extended Arnold-Liouville and noncommutative integrability to cosymplectic manifolds, proved a variant of non-commutative integrability for specific fields, constructed action-angle variables.
result Variant of non-commutative integrability for evaluation and Reeb vector fields on cosymplectic manifolds.
Extends Dirac structures to infinite dimensions, focusing on convenient Lie algebroids and manifolds.
problem Extending classical geometrical results from finite to infinite dimensions.
method Introduces partial Dirac structures on convenient Lie algebroids and manifolds, explores their properties and limits.
result Classical geometrical results can be extended to infinite dimensional contexts.
We extend Turaev's definition of torsion invariants of 3-dimensional manifolds equipped with non-singular vector fields, by allowing (suitable) tangency circles to the boundary, and manifolds with non-zero Euler characteristic. We show that these invariants apply in particular to (the exterior of) Legendrian links in c…
Extends Palais' result on diffeomorphisms to homeomorphisms and bi-Lipschitz mappings.
problem Extending diffeomorphisms to global mappings of manifolds.
method Elementary argument for diffeomorphisms, deep results for homeomorphisms and bi-Lipschitz mappings.
result Extension of Palais' result to homeomorphisms and bi-Lipschitz mappings.
Paper proves non-extendability of quasimorphism and non-vanishing of Reznikov's class.
problem Non-extendability of Shelukhin's quasimorphism and non-vanishing of Reznikov's class.
method Analyzing specific symplectic manifolds like blow-ups of tori and products of surfaces.
result Non-extendability of Shelukhin's quasimorphism and non-vanishing of Reznikov's class for certain symplectic manifolds.
Wall's result extended to 4-manifolds with definite intersection forms.
problem Realizing automorphisms of definite intersection forms.
method Using a specific 4-manifold construction and Wall's original result.
result Automorphisms of definite intersection forms are realized by diffeomorphisms of the constructed 4-manifold.
Extends cohomology to incomplete Riemannian manifolds.
problem Cohomology of harmonic forms on incomplete Riemannian manifolds.
method Abstract setting of Hilbert complexes.
result Geometric applications to Thom-Mather spaces.
We consider differential operators acting on densities of arbitrary weights on manifold M identifying pencils of such operators with operators on algebra of densities of all weights. This algebra can be identified with the special subalgebra of functions on extended manifold M^. On one hand there is a canonical…
We extend the link between Einstein Sasakian manifolds and Killing spinors to a class of η-Einstein Sasakian manifolds, both in Riemannian and Lorentzian settings, characterising them in terms of generalised Killing spinors. We propose a definition of supersymmetric M-theory backgrounds on such a geometry and find a …
Framework extends sutured manifold invariants to pairs with torus boundaries.
problem Extending sutured manifold invariants to pairs with torus boundaries.
method Establishing a framework for extending invariants of sutured manifolds to pairs of sutured manifolds differing by attaching a basic slice along a torus boundary.
result Framework recovers bordered-sutured Floer homology for a corresponding bordered-sutured three-manifold.
There are known infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. In this paper we show that free periodic actions on these Brieskorn spheres do not extend smoothly over a contractible 4-manifold. We give a new infinite family of examples in which …