Computing unlinking number is usually very difficult and complex problem, therefore we define BJ-unlinking number and recall Bernhard-Jablan conjecture stating that the classical unknotting/unlinking number is equal to the BJ-unlinking number. We compute BJ-unlinking number for various families of knots and links for w…
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “singular Björling problem”
New proof of timelike minimal surfaces using split-harmonic maps.
problem Interpolating a split-Fourier curve to a timelike minimal surface.
method Using split-harmonic maps to solve the singular Björling problem.
result Solved the interpolation problem for timelike minimal surfaces.
Constructs moduli spaces for Calabi-Yau cones and Sasaki-Einstein manifolds.
problem Proper moduli spaces for K-polystable Q-Fano cones and their links.
method Algebraic construction using local normalized volume and higher Θ-stable reduction.
result Alternative algebraic proof of proper moduli spaces for Q-Fano varieties.
Proposes a new Q-learning method for survival outcomes in clinical trials.
problem Incomplete follow-up data and nonlinear covariate effects in clinical trials.
method Combines Buckley-James boosting with flexible base learners for estimating optimal treatment regimes.
result Improves treatment decision accuracy and stability in longitudinal clinical trials.
Projection maps which appear in the theory of buildings and oriented matroids are closely related to the notion of shellability. This was first observed by Bj{ö}rner. In this paper, we give an axiomatic treatment of either concept and show their equivalence. We also axiomatize duality in this setting. As applications o…
A hypercomplex manifold M is a manifold with a triple I,J,K of complex structure operators satisfying quaternionic relations. For each quaternion L=aI +bJ+cK, L^2=-1, L is also a complex structure operator on M, called an induced complex structure. We are studying compact complex subvarieties of (M,L), when L is a gene…
Twistor space of hypercomplex manifolds is never Moishezon.
problem Characterize the twistor space of compact hypercomplex manifolds.
method Analyzing the twistor family and its total space.
result The twistor space of a compact hypercomplex manifold is never Moishezon.
Developed MF-PINNs to solve coupled Stokes-Darcy equations more accurately.
problem Solving coupled Stokes-Darcy equations with varying physical constants.
method Combining VP and SV forms with adjusted weights in MF-PINNs.
result Improved accuracy of streamline and pressure fields in numerical experiments.
Paper finds singular solutions for a specific physics problem on a sphere.
problem Existence of singular solutions to the conformal Dirac-Einstein system.
method Constructs a family of singular solutions on the 3D sphere.
result Constructs solutions with exactly two singularities.
Solves Deligne-Simpson problem for special connections on Gm.
problem Existence of Fuchsian connections with specific singularities.
method Theory of fundamental and regular strata, lattice chain filtration, quiver varieties.
result Characterization of rigid connections with unipotent monodromy at infinity.
This is a survey article on recognition problem of frontal singularities. We specify geometrically several frontal singularities and then we solve the recognition problem of such singularities, giving explicit normal forms. We combine the recognition results by K. Saji and several arguments on openings, which was perfo…
Study asymptotic behaviors of solutions near singular boundaries for the Yamabe problem.
problem Boundary behavior of the singular Yamabe problem near singular boundaries.
method Analysis of asymptotic behaviors and derivation of optimal estimates for background metrics.
result Solutions are well approximated by solutions in tangent cones at singular points.
Maxfaces can have cuspidal edges near certain singularities.
problem Characterizing singularities on maxfaces.
method Analyzing singular Björling data and proving geometric properties.
result Near a maxface with a specific type of singularity, there exists another maxface with a cuspidal edge.
Study integrability of generalized almost complex structures on S^6.
problem Integrability of generalized almost complex structures on the 6-dimensional sphere.
method Local coordinate criteria for integrability with respect to brackets and Courant integrability for strong structures.
result No nontrivial spherical combinations of the canonical structures are integrable with respect to the Levi-Civita connection.
Improved estimates for singularities in capillary surfaces.
problem Understanding the singularities of minimizing capillary hypersurfaces.
method Improved estimates based on connections to the one-phase Bernoulli problem.
result The singular set is of codimension at least 4, improving for specific angles.
Singular recursive utilitymath.OC
We introduce the concept of singular recursive utility. This leads to a kind of singular BSDE which, to the best of our knowledge, has not been studied before. We show conditions for existence and uniqueness of a solution for this kind of singular BSDE. Furthermore, we analyze the problem of maximizing the singular rec…
Paper solves curvature assignment on surfaces with sharp points and edges.
problem Prescribing curvatures on surfaces with conical singularities and corners.
method New variational formulation for surfaces with singularities.
result First results for prescribed curvatures on surfaces with singularities.
This is Part 1 of two papers where we develop the basic potential theory of elliptic operators on posssibly singular almost minimzers using their hyperbolic unfoldings. We can establish surprisingly robust boundary Harnack inequalities along the singular set. We apply them to derive a Martin theory and solve classical …
Sharp bound on singular set dimension for specific geometric problems.
problem Hausdorff dimension of singular set in free boundary problems.
method Analysis of noncollapsed limits of manifolds with Ricci curvature bounds.
result Dimension bound of singular set is .
New scalars measure failure of CC metrics to solve singular Yamabe problem.
problem Measuring failure of CC metrics to solve singular Yamabe problem.
method Introducing conformally invariant scalar curvature quantities along conformal infinity.
result CC boundary curvature scalars compute canonical expansion coefficients for singular Yamabe metrics.
New algorithm for Coxeter connections with maximally ramified singularities.
problem Constructing connections on the projective line with a maximally ramified irregular singularity.
method Numerical algorithm for matrix completions to solve the Upper Nilpotent Completion Problem.
result Explicit constructions of Coxeter connections with specified singularities.
Given a closed Riemannian manifold and a nonempty closed subset in , the singular Yamabe problem asks for a complete metric on conformal to with constant curvature. The curvature is defined as the th elementary symmetric function of the eigenvalues of the…
Paper calculates Morse index of Y-singular minimal surfaces.
problem Computing Morse index of Y-singular minimal surfaces.
method Utilized two simpler problems: fixed boundary problem and Dirichlet-to-Neumann map.
result Index of Y-catenoid is one.
Paper solves the minimal generating set problem for singular Reidemeister moves.
problem Determine minimal generating sets of oriented singular Reidemeister moves.
method Introduced new invariant for singular links to detect type IV moves and provide obstructions.
result Proved exactly 96 distinct inclusion-minimal generating sets for singular moves.
This paper solves part of a problem by constructing surfaces with specific curvature and singularities.
problem Solving an open problem by Gálvez, Hauswirth, and Mira regarding constant curvature metrics with conical singularities.
method Established a geometric correspondence between metrics and isometric immersions into Euclidean 3-space, constructing a family of surfaces.
result Explicitly constructed a family of surfaces with constant curvature one and two conical singularities.
Study on mean curvature flow through singularities in 3D and 4D.
problem Understanding mean curvature flow through singular points.
method General introduction and classification of singularities in and .
result Classification of all noncollapsed singularities in .
Paper proves conditions for rational homology complex projective planes with singularities.
problem Proving conditions for rational homology complex projective planes with singularities.
method Leveraging results from smooth 4-manifolds, including Donaldson diagonalization theorem and Heegaard Floer correction terms.
result Eliminates the possibility of a rational homology complex projective plane with four singularities and identifies families of singularities obstructed by smooth conditions.
This paper is devoted to the construction of weak solutions to the singular constant -curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) -curvature.
Constructs singular Yamabe solutions via equivariant reduction.
problem Constructs non-trivial geometric examples for the Yamabe equation.
method Reduces the problem to an equivariant setting for simpler analysis.
result Provides a non-trivial weak solution to the Yamabe problem.
Solves initial value problem for harmonic maps on specific manifolds.
problem Initial value problem for harmonic maps on cohomogeneity one manifolds.
method Setup and solve the initial value problem using equivariant harmonic maps and regular-singular systems.
result Local existence of harmonic maps in a neighborhood of singular orbits.
In this note, we present some interesting observations on the Schiffer's conjecture, interior transmission eigenvalue problem and their connections to singular and nonsingular invisibility cloaking problems of acoustic waves.
This paper explores how local behavior of meromorphic connections on the projective line determines the global connection.
problem Determining the global meromorphic connection based on specified local behavior at singular points.
method Expository discussion of various problems related to meromorphic connections with specified local behavior, including Deligne-Simpson and rigidity problems.
result The existence and nonemptiness of moduli spaces of meromorphic connections with specified local behavior.
The paper solves conditions for non-singular extensions of fold maps.
problem Conditions for the existence of non-singular extensions of horizontal stable fold maps.
method Defined a combinatorial object called a pairing map to prove equivalence of existence.
result Existence of non-singular extensions is equivalent to the existence of a pairing map.
The paper studies harmonic maps to the circle with complex singular sets.
problem Finding harmonic maps with prescribed singular sets in higher-dimensional spaces.
method Considered variational relaxations of the problem, showing energy convergence to a renormalised volume plus lower-order interaction energy.
result The energy of minimisers converges, after renormalisation, to the volume of the singular set plus a lower-order interaction energy.
New solutions found for Yamabe problem on spheres with foliations.
problem Yamabe problem on spheres with singular Riemannian foliations.
method Variational methods, symmetries from foliations, Sobolev embedding theorem, Principle of Symmetric Criticality.
result Existence of sign-changing and positive solutions with specific symmetries.
We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex proje…
We investigate the singular sets of solutions of conformally covariant elliptic operators of fractional order with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe problem.
In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of holonomy transformation. Unlike the regular case, holonomy transformations can not be…
Solved a conjecture about rational homology projective planes with quotient singularities.
problem A conjecture about rational homology projective planes with quotient singularities.
method Combining Donaldson's diagonalization theorem with a distinguished spin^c structure on the smooth locus.
result Proved that rational homology projective planes with quotient singularities have at most three singular points.
Solves Plateau-Douglas problem for singular configurations in general metric spaces.
problem Existence of minimal surfaces for singular configurations.
method Generalized approach via minimal sequences in metric spaces.
result Existence of minimal surfaces for singular configurations in general metric spaces.
A second order linear integro-differential equation with Volterra integral operator and strong singularities at the endpoints (zero and infinity) is considered. Under limit conditions at the singular points, and some natural assumptions, the problem is a singular initial problem with limit normalizing conditions at inf…
We prove well-posedness and regularity results for elliptic boundary value problems on certain domains with a smooth set of singular points. Our class of domains contains the class of domains with isolated oscillating conical singularities, and hence they generalize the classical results of Kondratiev on domains with c…
Fast and accurate methods for low-rank learning problems.
problem Partial singular value decomposition and numerical rank estimation of huge matrices.
method Krylov subspaces and Ritz vectors for fast and accurate solutions.
result Advantages over traditional methods in accuracy and speed.
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behaviour of the surfaces at the big cell boundary,…
In this paper we study the problem of existence of orbifold Kaehler-Einstein metrics on del Pezzo surfaces of degree 1 with Du Val singular points. Moreover we compute global log canonical thresholds of del Pezzo surfaces of degree 1 with Du Val singularities and of del Pezzo surfaces of Picard rank 1 with Du Val singu…
Analyzes singularities of convex hypersurfaces in hyperbolic space.
problem Understanding singularities of convex hypersurfaces with constant curvature.
method Analyzes the structure of singular sets using convex curvature functions.
result Describes the structure of singular sets in hyperbolic space.
Study geometric equations on cohomogeneity one manifolds near singular orbits.
problem Solving geometric equations like Ricci, Einstein, and soliton near singular orbits.
method Special assumption simplifies proof; general case solved in Part II.
result Existence and uniqueness of solutions near singular orbits.
In this paper, we develop the blow-up analysis and establish the energy quantization for solutions to super-Liouville type equations on Riemann surfaces with conical singularities at the boundary. In other problems in geometric analysis, the blow-up analysis usually strongly utilizes conformal invariance, which yields …