It is shown that every subcritical Stein manifold is deformation equivalent to the product of a Stein manifold with $\C$.
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48 results for “Stein deformation”
In this note, we classify Stein fillings of an infinite family of contact 3-manifolds up to diffeomorphism. Some contact 3-manifolds in this family can be obtained by Legendrian surgeries on along certain Legendrian 2-bridge knots. We also classify Stein fillings, up to symplectic deformation, of an inf…
Let X be a Stein manifold, A a closed complex subvariety of X, and f a continuous map from X to a complex manifold Y whose restriction to A is holomorphic. After a homotopic deformation of the Stein structure outside a neighborhood of A in X (and of its smooth structure when X is a Stein surface)we find a holomorphic m…
Survey on Stein manifolds embeddings and immersions, including a new result.
problem Existence of holomorphic embeddings and immersions of Stein manifolds.
method Survey and inclusion of a new result involving homotopy and Stein structures.
result Every continuous map between Stein manifolds is homotopic to a proper holomorphic embedding under certain conditions.
Complete negative Kähler-Einstein metric found on Stein manifolds.
problem Existence of complete Kähler-Einstein metrics on Stein manifolds with negative curvature.
method Normalized Kähler-Ricci flow to deform metrics to complete negative Kähler-Einstein metric.
result Existence of complete negative Kähler-Einstein metric on Stein manifolds with negatively pinched holomorphic sectional curvature.
The paper extends local h-principles to complex structures on Stein manifolds.
problem Existence of local h-principles for complex structures on Stein manifolds.
method Introducing realifications of partial holomorphic relations and proving h-principles for them.
result Local h-principles can be extended to complex structures on Stein manifolds.
New Stein fillings found for rational surface singularities.
problem Exploring Stein fillings of rational surface singularities.
method Using planar open books and Lefschetz fibrations, describe Stein fillings via symplectic disk arrangements.
result Many rational singularities admit Stein fillings not diffeomorphic to Milnor fibers.
On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classificationmath.SG
This paper classifies symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
problem Classifying symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions.
method Using holomorphic curves and Lefschetz fibrations to classify fillings.
result Symplectic and Stein fillings of contact 3-manifolds with spinal open book decompositions can be classified up to deformation equivalence.
In this article, using combinatorial techniques of mapping class groups, we show that a Stein fillable integral homology -sphere supported by an open book decomposition with page a -holed sphere admits a unique Stein filling up to diffeomorphism. Furthermore, according to a property of deforming symplectic fillin…
We prove that every continuous map from a Stein manifold X to a complex manifold Y can be made holomorphic by a homotopic deformation of both the map and the Stein structure on X. In the absence of topological obstructions the holomorphic map may be chosen to have pointwise maximal rank. The analogous result holds for …
The study translates Weinstein structures to Legendrian handlebodies for symplectic topology.
problem Detecting flexibility and rigidity in Weinstein manifolds.
method Systematic recipe for translating Weinstein Lefschetz fibrations to Legendrian handlebodies.
result Verification of Stein deformation equivalence and existence of closed exact Lagrangian submanifolds.
Extensions and Applications of Stein-Weiss Operators to the Study of Traceless Symmetric Tensorsmath.DG
The paper studies Stein-Weiss operators on symmetric tensors, extending previous work.
problem Understanding Stein-Weiss operators on symmetric tensors of arbitrary rank.
method Analyzing the decomposition of tensor spaces into irreducible components and computing Weitzenbock formulas.
result Unified framework for second-order Stein-Weiss operators and tools for geometric analysis.
New method constructs deformation groupoid for inhomogeneous pseudo-differential calculus.
problem Recovering inhomogeneous pseudo-differential calculus using a deformation groupoid.
method Elementary construction of deformation groupoid for Heisenberg calculus, then generalization to arbitrary filtrations.
result Elementary construction of deformation groupoid for inhomogeneous pseudo-differential calculus.
We construct new complete Einstein metrics on smoothly bounded strictly pseudoconvex domains in Stein manifolds. This is done by deforming the Kähler-Einstein metric of Cheng and Yau, the approach that generalizes the works of Roth and Biquard on the deformations of the complex hyperbolic metric on the unit ball. Recas…
Study symplectic fillings of sandwiched singularities.
problem Contrast deformation theory and symplectic topology of Milnor fibers.
method Develop an analog of de Jong--van Straten's theory in the symplectic setting using spinal open books and nearly Lefschetz fibrations.
result Minimal symplectic fillings of links are generated by certain immersed disk arrangements.
This paper concerns with deformations of noncompact complex hyperbolic manifolds (with locally Bergman metric), varieties of discrete representations of their fundamental groups into and the problem of (quasiconformal) stability of deformations of such groups and manifolds in the sense of L.Bers and D.Sulliva…
We study deformations of complex hyperbolic surfaces which furnish the simplest examples of: (i) negatively curved Kähler manifolds and (ii) negatively curved Riemannian manifolds not having {\it constant} curvature. Although such complex surfaces may share the rigidity of quaternionic/octionic hyperbolic manifolds, ou…
A locally conformally Kähler (LCK) manifold is one which is covered by a Kähler manifold with the deck transform group acting conformally on . If admits a holomorphic flow, acting on conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vais…
Stein's method improves probabilistic inference and learning.
problem Improving probabilistic inference and learning methods.
method Constructing Stein discrepancies from Stein operators and Stein sets, discussing their properties.
result Connection between Stein operators and Stein variational gradient descent.
We prove symplectic hypersurfaces in Weinstein domains and give obstructions for manifold boundaries.
problem Obstructions for 3-manifolds to bound Weinstein domains in certain symplectic 4-manifolds.
method Symplectic embedding and deformation techniques.
result Obstructions for 3-manifolds to bound Weinstein domains in rational surfaces.
GC Stein manifolds characterized with embeddings and functions.
problem Characterize GC Stein manifolds using embeddings and functions.
method Extended Cartan's Theorem A and B, defined -plurisubharmonic functions, established GH embeddings.
result Characterized GC Stein manifolds via -plurisubharmonic exhaustion functions and GH embeddings.
Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
Extends Stein's lemma to exponential-family mixtures for gradient computation.
problem Computing gradients for complex distributions with weak assumptions.
method Generalizes Stein's lemma to exponential-family mixtures and applies it to reparameterization trick.
result Derives new gradient identities for various distributions.
We give a bordism-theoretic characterisation of those closed almost contact (2q+1)-manifolds (with q > 2) which admit a Stein fillable contact structure. Our method is to apply Eliashberg's h-principle for Stein manifolds in the setting of Kreck's modified surgery. As an application, we show that any simply connected a…
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
Develops Stein's method for Riemannian manifolds using diffusion.
problem Bounding integral metrics on probability measures on Riemannian manifolds.
method Exploits the relationship between diffusion generators and Stein operators to derive Stein factors.
result Derives curvature-dependent Stein factors that generalize existing results for Euclidean spaces.
Regularized Stein thinning improves MCMC output approximations.
problem Pathologies in Stein thinning leading to poor approximations.
method Theoretical analysis and regularization to improve KSD.
result Regularized Stein thinning alleviates pathologies and improves efficiency.
Study Stein and Milnor fillings of links from surface singularities.
problem Comparing Stein and Milnor fillings of links from surface singularities.
method Analyzing the topology and obstructions of Stein fillings and Milnor fillings.
result Milnor fillings have bounded topology, while Stein fillings can be more varied.
New contact manifolds have many ways to be filled.
problem Understanding infinitely many ways to fill contact manifolds.
method Constructing specific contact manifolds and proving they have many Stein fillings.
result Contact manifolds have infinitely many ways to be filled.
Stein transport improves Bayesian inference with faster convergence and reduced variance.
problem Efficiently approximating posterior distributions in Bayesian inference.
method A novel Bayesian inference method using Stein transport, which pushes particles along a curve of tempered distributions.
result Stein transport reaches posterior approximations faster and more accurately than Stein variational gradient descent (SVGD).
The paper improves Stein importance sampling for Markov chain samples.
problem Improving the accuracy of sampling from complex distributions.
method Reproducing Stein kernels approach for post-hoc correction.
result Consistent estimators for target distributions using geometrically ergodic Markov chains.
Counterexample found for Stein property of certain solvable Lie groups.
problem Stein property of simply connected unimodular solvable Lie groups with left-invariant complex structures.
method Constructing a solvable Lie group with specific properties.
result A simply connected solvable Lie group with a left-invariant complex structure whose universal cover is not Stein.
Stein Pointsstat.CO
Stein Points improve posterior approximation with minimal points.
problem Approximating posterior distributions with limited points.
method Greedy or conditional gradient method to minimize kernel Stein discrepancy.
result Stein Points enable accurate approximation at low computational cost.
SVGD uses particle transport to approximate distributions, with theoretical guarantees.
problem Approximating complex distributions efficiently.
method Iterative particle transport guided by gradient of KL divergence.
result SVGD's asymptotic behavior is a gradient flow under a new metric.
A new framework improves kernel Stein discrepancy tests for validating distributions.
problem Improving goodness-of-fit testing for non-normal distributions.
method Introducing Sf-KSD, a unifying framework for studying Stein operators in KSD-based tests.
result Sf-KSD guides the development of new tests and outperforms existing methods.
We show that, under a certain condition, contact 5-manifolds can `coarsely' distinguish smooth structures on compact Stein 4-manifolds via contact open books. We also give a simple sufficient condition for an infinite family of Stein 4-manifolds to have an infinite subfamily of pairwise non-diffeomorphic Stein 4-manifo…
2-stein submanifolds in space forms have constant curvature if normal connection is flat or codimension is 2.
problem Characterizing submanifolds with constant curvature in space forms.
method Analyzing submanifolds with flat normal connection or codimension 2.
result 2-stein submanifolds have constant curvature under specified conditions.
New KCC-SDs improve distribution comparison in high dimensions.
problem Challenges in high-dimensional Stein discrepancies.
method Kernelized complete conditional Stein discrepancies (KCC-SDs).
result KCC-SDs outperform baselines in distinguishing distributions.
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
problem The curse-of-dimensionality in kernelized Stein discrepancy (KSD).
method Sliced Stein discrepancy and its scalable variants using optimal one-dimensional projections.
result Significantly outperforms KSD and baselines in goodness-of-fit tests and improves model learning.
The study finds knots with Stein structures beyond the typical upper bound.
problem Finding knots with Stein structures beyond the known upper bound.
method Constructing specific knots and framings to demonstrate Stein structures.
result The largest framing for which a knot admits a Stein structure can be arbitrarily larger than the usual upper bound.
We give an algorithm which produces infinitely many pairwise exotic Stein fillings of the same contact 3-manifolds, applying positive allowable Lefschetz fibrations over the disk. As a corollary, for a large class of Stein fillings, we realize the topological invariants (i.e. fundamental group, homology group, homology…
The square root of Fredholm determinants causes numerical instabilities in option pricing models.
problem Numerical instabilities in Fourier-based option pricing for the Volterra Stein-Stein model.
method Characterization of determinant crossing behavior, derivation of transform to handle crossings, efficient algorithms.
result Significant improvement in accuracy and reduction in computational cost for Fourier-based pricing.
Stein Variational Gradient Descent optimizes particle sets to match distribution expectations.
problem Efficiently approximating complex distributions in machine learning.
method Evolve particle sets to match the expectations of a given distribution using Stein operators and kernels.
result Particles can be used to exactly estimate expectations of functions on distributions, providing insights into kernel choice.
Study Stein fillings of planar contact 3-manifolds with relative trisection genus 2.
problem Classify Stein fillings of planar contact 3-manifolds under constraints on their relative trisections.
method Partial classification of diffeomorphism types of fillings with relative trisections of genus at most 2.
result Partially classify the diffeomorphism types of Stein fillings with relative trisections of genus at most 2.
Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
problem Improving scalability and stability of Stein discrepancies for scalable goodness-of-fit testing
method Reformulating Stein discrepancy construction as an explicit SNR^2 maximisation problem
result Avoiding exponential SNR^2 collapse and achieving stable SNR^2
Study continuity and Hölder estimates for solutions on Stein spaces.
problem Continuity and Hölder estimates for solutions to degenerate complex Monge-Ampère equations.
method Prove continuity up to the boundary and local Hölder estimates on the regular locus.
result Local Hölder estimates on the regular locus for solutions to degenerate complex Monge-Ampère equations.
Paper proves existence of compatible Lefschetz fibrations on 6-ball and Stein domains.
problem Existence of compatible Lefschetz fibrations on Stein domains.
method Topological proof for 6-ball fibrations, construction of relative Stein pairs.
result Existence of compatible Lefschetz fibrations on Stein domains of dimension six.
Stein Variational Gradient Descent optimizes Bayesian inference efficiently.
problem Efficient Bayesian inference for complex models.
method Iteratively transports particles to match target distribution using KL divergence minimization.
result Competitive with state-of-the-art methods on various real-world models.