Study complex quaternionic manifolds and their c-projective structures.
problem Characterize connections on quaternionic manifolds with specific holonomy.
method Quaternionic Feix--Kaledin construction and analysis of c-projective classes.
result Characterize distinguished connections in quaternionic manifolds.
Local classification of quaternion-Kähler metrics with rotating S1-symmetry.
problem Classifying quaternion-Kähler metrics with specific symmetries.
method Quaternionic Feix--Kaledin construction and explicit construction of holomorphic contact distributions.
result Quaternion-Kähler metrics with rotating S1-symmetry are determined by a Kähler metric and a line bundle. Study of a metric on cotangent bundle spaces of Kähler quotients.
problem Construct and analyze a metric on the total space of cotangent bundles to Kähler quotients.
method Use hyperkähler reduction to construct a hyperkähler metric, prove its coincidence with the Feix-Kaledin metric, and investigate its completeness.
result The metric completion of the space Y is a stratified hyperkähler space with an algebraic structure. The paper studies symmetries in quaternionic geometry and submanifolds.
problem Understanding symmetries in quaternionic geometry and their implications for submanifolds.
method Generalized Feix--Kaledin construction, infinitesimal symmetries analysis, quaternionic and c-projective symmetries study.
result Conditions for extending c-projective symmetries to quaternionic symmetries and studying specific hyperkähler structures.
Extends quaternionic constructions from complex manifolds to more general settings.
problem Construct quaternionic manifolds with circle actions from complex structures.
method Using twistor spaces and connections on line bundles, extend Feix-Kaledin construction.
result Constructs quaternionic manifolds with circle actions, including self-dual conformal 4-manifolds.
The paper generalizes hyperkahler metrics near Lagrangian submanifolds.
problem Constructing hyperkahler structures near complex Lagrangian submanifolds.
method Generalization of Feix-Kaledin theorem and deformations of holomorphic symplectic structures.
result Hyperkahler structures can be constructed on symplectic realizations of holomorphic Poisson manifolds.
The paper proves properties of a hyperkähler moduli space for surfaces with genus ≥ 2.
problem The hyperkähler moduli space of almost-Fuchsian structures on surfaces.
method Proofs using Teichmüller theory, Higgs bundles, and hyperbolic geometry.
result The hyperkähler structure on the moduli space extends the Weil-Petersson metric and Goldman symplectic structure.
We construct non-constructible simplicial d-spheres with d+10 vertices and non-constructible, non-realizable simplicial d-balls with d+9 vertices for d≥3.
New construction generalizes quaternionic Kähler/hyper-Kähler correspondence.
problem Constructing hypercomplex manifolds from quaternionic ones.
method Constructing hypercomplex manifold M′ from quaternionic manifold M with U(1)-symmetry. result Obtained a compact homogeneous hypercomplex manifold without hyper-Kähler structure.
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…
Modified curve shortening flow constructs λ-Angenent curve.
problem Constructing λ-Angenent curve. method Modified curve shortening flow
result Constructs λ-Angenent curve. Surveying isoparametric foliations and related geometric constructions.
problem Constructing isoparametric foliations using Clifford algebra.
method Representation theory of Clifford algebra and mean curvature flow.
result Investigation of geometric constructions related to isoparametric hypersurfaces.
Article constructs coassociative submanifolds in Joyce's G2-manifolds.
problem Constructing coassociative submanifolds in Joyce's G2-manifolds. method Using Joyce's generalised Kummer construction, focusing on the critical region where the metric degenerates.
result The volume of the coassociatives shrinks to zero as the orbifold-limit is approached.
The twist construction is a geometric model of T-duality that includes constructions of nilmanifolds from tori. This paper shows how one-dimensional foliations on manifolds may be used in a shear construction, which in algebraic form builds certain solvable Lie groups from Abelian ones. We discuss other examples of geo…
We describe various constructions in Sasakian geometry. First we generalize the join construction of the first two authors to arbitrary Sasakian manifolds. We then give several examples, including ones which prove the existence of Sasakian-Einstein metrics on manifolds homeomorphic to S2×S5. Then we use a gen…
Study calculates cohomology of G2-manifolds using Kummer construction.
problem Calculating the cohomology of G2-manifolds.
method Intersection theory applied to generalized Kummer construction.
result Generators and product structure of rational cohomology ring identified.
Unified framework for constructing RKBSs with various norms and kernels.
problem Unclear relations among existing RKBS constructions.
method Generic definition of RKBS and reproducing kernel, continuous bilinear form, feature maps.
result Unified framework unifies existing RKBS constructions and develops representer theorems.
Survey on constructing manifolds over simple polytopes using Lickorish's method.
problem Classifying manifolds over simple convex polytopes with torus action.
method Lickorish type construction over simple polytopes with torus action.
result Many classical classification results can be interpreted using this construction.
The paper constructs infinitely many surfaces with specific mean curvature.
problem Creating surfaces with prescribed mean curvature in the presence of a strictly stable minimal surface.
method Synthesizing ideas from previous constructions to create multiple surfaces.
result Infinitely many distinct surfaces with prescribed mean curvature are constructed.
We construct bi-invariant total orderings of residually torsion-free nilpotent groups by using Chen's iterated integrals. This construction can be seen as a generalization of the Magnus ordering of the free groups, and equivalent to the classical construction which uses an iteration of central extensions. Our geometric…
Explains a 1978 construction for Yang-Mills instantons.
problem None explicitly stated; focuses on explaining a construction.
method Atiyah-Drinfeld-Hitchin-Manin construction
result Explains the ADHM construction of Yang-Mills instantons.
We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the Metropolis-Hastings algorithm is constructed adaptively by changing the parameters of t…
We construct several non-trivial examples of CAT(1) spaces by using the idea of free construction.
New pseudomodular groups constructed from jigsaw construction.
problem Existence and properties of pseudomodular groups.
method Jigsaw construction of groups.
result Infinitely many simplest jigsaw groups are not pseudomodular.
Study constructs associative submanifolds in G2-manifolds from orbifolds.
problem Constructing associative submanifolds in G2-manifolds from orbifolds. method Using Joyce's generalised Kummer construction.
result The volume of associative submanifolds tends to zero as they approach orbifolds.
Test-asset construction affects factor model performance.
problem How test assets are constructed impacts factor model performance.
method Forming characteristic-unsorted random portfolios and varying stock selection, initial weighting, holding, and rebalancing.
result Test-asset construction shifts factor model rankings materially.
Survey on rigorous construction of supersymmetric path integral.
problem Rigorous construction of supersymmetric path integral.
method Construction based on joint work with collaborators.
result Rigorous construction of supersymmetric path integral.
New construction reveals group relationships for Klein quartic.
problem Understanding non-arithmetic ball quotients and their groups.
method Algebro-geometric construction of ball quotients.
result Reveals connections between orbifold fundamental groups and Klein quartic automorphism group.
We introduce the cutting construction of possibly non-compact symplectic toric manifolds, in particular, toric symplectic cones that correspond to a weakly convex good cone. Since the symplectization of a toric contact manifold is a toric symplectic cone, we can also construct toric contact manifolds that correspond to…
Researchers match complex affine structures in mirror constructions.
problem Matching complex affine structures in SYZ fibrations of Del Pezzo surfaces.
method Floer-theoretical gluing method to construct mirrors using immersed Lagrangians.
result The constructed mirror agrees with Carl-Pomperla-Siebert's mirror.
We construct calibrated submanifolds of R^7 and R^8 by viewing them as total spaces of vector bundles and taking appropriate sub-bundles which are naturally defined using certain surfaces in R^4. We construct examples of associative and coassociative submanifolds of R^7 and of Cayley submanifolds of R^8. This construct…
Extends knot surgery to exotic four-manifolds.
problem Constructing exotic definite four-manifolds.
method Generalizes RBG construction to n-surgery. result Produces pairs of knots with same n-surgery. The paper constructs solutions to a critical Dirac equation on spheres.
problem Solving the critical Dirac equation on spheres with singularities.
method Constructing Delaunay-type solutions and another kind of singular solutions.
result The constructed solutions are building blocks for singular solutions on Spin manifolds.
In this paper, we construct the index bundle gerbe of a family of self-adjoint Dirac-type operators, refining a construction of Segal. In a special case, we construct a geometric bundle gerbe called the caloron bundle gerbe, which comes with a natural connection and curving, and show that it is isomorphic to the analyt…
Two constructions link path geometries to almost Grassmann structures.
problem Linking path geometries to almost Grassmann structures.
method Introducing two Fefferman-type constructions.
result Characterizing conditions for almost Grassmann structures arising from these constructions.
New naturally reductive spaces constructed with group isometries.
problem Creating new naturally reductive spaces.
method Constructing infinitesimal models, specifying transitive groups of isometries, and explicitly defining the naturally reductive structure.
result A large number of new naturally reductive spaces constructed.
New explicit constructions of unbalanced Ramanujan bipartite graphs.
problem Constructing bipartite Ramanujan graphs with specified degrees and avoiding certain edges.
method Presented explicit constructions and discussed known methods for Ramanujan graph construction.
result Affirmative answer to constructing unbalanced Ramanujan bipartite graphs under certain conditions.
Constructs subvarieties in translation surface strata using combinatorial input.
problem Creating subvarieties in translation surface strata.
method Combining Hurwitz spaces theory with combinatorial input.
result Constructs Teichmueller curves and orbit closures.
Viscosity method constructs geodesics on manifolds.
problem Construct closed geodesics on compact Riemannian manifolds.
method Viscosity approach to min-max construction.
result Lower semi-continuity of geodesic index proved.
Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification Khovanov provides a topological construction of (n/2,n/2) Springer varieties. We extend Khovanov's construction to all two-row Springer varieties. Using the combinatorial and diagrammatic …
Constructs nonarithmetic hyperbolic manifolds with specific properties.
problem Creating nonarithmetic hyperbolic manifolds.
method Inbreeding construction with specific hyperplanes.
result Infinitely many non-commensurable nonarithmetic manifolds constructed.
Constructs harmonic maps between special geometric shapes.
problem Creating harmonic maps between specific types of geometric shapes.
method Equivariant harmonic maps constructed between cohomogeneity one manifolds.
result Developed a method to construct harmonic maps.
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a geometric construct of a modular functor for any simple Lie-algebra and any level…
Paper proposes NNAFC for automatic financial factor construction.
problem Manual factor construction is time-consuming and prone to bias.
method NNAFC uses neural networks to automatically construct diversified financial factors.
result NNAFC outperforms GP in constructing more informative and diversified factors.
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to prolong the Riemannian connection from the tangent bundle into the spinor one w…
Constructs surfaces with specific topologies and curvatures.
problem Creating surfaces with prescribed genus and ends.
method Using a family of constant mean curvature surfaces constructed in \cite{Kleene}, resolving tangency points over catenoidal necks.
result Complete embedded surfaces with freely prescribed genus and ends.
Geometric model for Hodge filtered complex cobordism constructed.
problem Constructing a geometric model for Hodge filtered complex cobordism.
method Refinement of Pontryagin-Thom construction to create an explicit isomorphism.
result Explicit isomorphism between geometric and abstract models for complex manifolds.
Paper constructs naturally reductive spaces with a general formula.
problem Understanding naturally reductive spaces.
method Explicit construction from \cite{Storm2018} and general formula derivation.
result Proves reducibility and isomorphism criteria.