Extends cutting and blowing up to nonrational symplectic settings.
problem Nonrational symplectic toric structures.
method Cutting and blowing up in nonrational directions.
result Extension to symplectic toric manifolds and orbifolds.
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48 results for “cutting and blowing up”
In this paper, using the gluing formula of Gromov-Witten invariants under symplectic cutting, due to Li and Ruan, we studied the Gromov-Witten invariants of blow-ups at a smooth point or along a smooth curve. We established some relations between Gromov-Witten invariants of M and its blow-ups at a smooth point or along…
The paper derives a formula for Chow weights of toric blow-ups.
problem Chow weights of toric blow-ups.
method Combinatorial formula derived from toric manifold and Delzant polytope.
result Explicit formula for Chow weights of blow-ups.
Nilpotent groups can't be biLipschitz embedded into .
problem Proving that simply connected nilpotent Lie groups cannot be biLipschitz embedded into .
method Using a pull-back distance and cut measures, the authors show that bi-Lipschitz embeddings can't exist in non-abelian settings.
result Every Carnot group that biLipschitz embeds into is abelian.
We study the small time asymptotics of the gradient and Hessian of the logarithm of the heat kernel at the cut locus, giving, in principle, complete expansions for both quantities. We relate the leading terms of the expansions to the structure of the cut locus, especially to conjugacy, and we provide a probabilistic in…
Study curve shortening flow in high dimensions with boundary constraints.
problem Understanding the behavior of curves in high-dimensional spaces with boundary conditions.
method Used curvature and higher-derivative estimates, Stahl-type maximum principle, and blow-up analysis.
result Flow converges to a shrinking semicircle model or has only semicircle boundary singularities in low entropy regimes.
We define a new 4-dimensional symplectic cut and paste operation which is analogous to Fintushel and Stern's rational blow-down. We use this operation to produce multiple constructions of symplectic smoothly exotic complex projective space blown-up eight times, seven times, and six times. We also show how this operatio…
We give finiteness results and some classifications up to diffeomorphism of minimal strong symplectic fillings of Seifert fibered spaces over S^2 satisfying certain conditions, with a fixed natural contact structure. In some cases we can prove that all symplectic fillings are obtained by rational blow-downs of a plumbi…
We express the Connes-Chern character of the Dirac operator associated to a b-metric on a manifold with boundary in terms of a retracted cocycle in relative cyclic cohomology, whose expression depends on a scaling/cut-off pa- rameter. Blowing-up the metric one recovers the pair of characteristic currents that represent…
Study blow-ups of locally conformal symplectic manifolds.
problem Blow-ups of locally conformal symplectic manifolds.
method Show existence of locally conformal symplectic structure on blow-ups.
result Existence of locally conformal symplectic structure on blow-ups.
Study blow-ups in generalized complex geometry using holomorphic ideals.
problem Blow-ups in generalized complex geometry.
method Introduce holomorphic ideal to define blow-ups in smooth manifolds. Identify suitable submanifolds and provide conditions for blow-ups.
result Necessary and sufficient conditions for generalized Poisson submanifolds to carry a canonical holomorphic ideal and for blow-ups to be generalized complex.
Study on half spheres solves Nirenberg problem with complex blow-up analysis.
problem Prescribing scalar curvature on half spheres.
method Refined blow-up analysis of finite energy approximated solutions.
result Complex blow-up points and vortex problems reveal new connections.
The paper defines and constructs almost complex blow-ups on 4D almost complex manifolds.
problem Existence and uniqueness of almost complex blow-ups on almost complex manifolds.
method Definition and construction of almost complex blow-ups, proving their existence and uniqueness.
result Existence and uniqueness of almost complex blow-ups on 4D almost complex manifolds.
Formula derived for holomorphic Poisson blow-ups.
problem Invariance of Koszul-Brylinski homology under Poisson blow-ups.
method Blow-up formula derivation for holomorphic Koszul-Brylinski homologies.
result Invariance of -degeneracy of Dolbeault-Koszul-Brylinski spectral sequence.
Study identifies numerical signs of blow-up in hydrodynamic equations.
problem Determining if numerical results of blow-up are genuine or artifacts.
method Geometrically consistent spatiotemporal discretization of complexified Euler equations.
result Identification of a signature based on supremum norm growth rates of vorticity.
Formula derived for Bott-Chern classes in complex blow-ups.
problem Calculating Bott-Chern classes in blow-ups of complex manifolds.
method Proved blow-up formula for Bott-Chern classes, established Riemann-Roch without denominators.
result Formula for Bott-Chern classes in blow-ups.
Explains blow-ups for Lie groupoids and algebroids, comparing different methods.
problem Blow-ups of Lie groupoids and algebroids.
method Detailed explanation of various blow-up constructions.
result Different blow-up constructions for Lie groupoids and algebroids are shown to fit into a general geometric framework.
Study of blow-ups in generalized Kähler geometry with specific conditions.
problem Blow-ups in generalized Kähler manifolds with generalized Poisson submanifolds.
method Blow-up theory for generalized Kähler manifolds, lifting bi-Hermitian structure, deformation procedure based on potentials.
result Degenerate bi-Hermitian structure on blow-up can be deformed into non-degenerate structure.
New proof of blow-up formula for Morse-Novikov cohomology.
problem Blow-up formula for Morse-Novikov cohomology.
method Introducing relative Morse-Novikov cohomology and using sheaf cohomology.
result Explicit isomorphism in relative Morse-Novikov cohomology.
Study on curvature blow-up rates in black hole interiors from gravitational collapse.
problem Understanding curvature blow-up rates in black hole interiors during gravitational collapse.
method Investigation of spherically symmetric Einstein-scalar field spacetimes, focusing on blow-up rates of curvature and mass.
result Kretschmann scalar blows up faster than in Schwarzschild setting, indicating a new blow-up phenomenon.
Computes cohomologies of blow-ups and projective bundles.
problem Cohomologies of blow-ups and projective bundles.
method Computes double complex of differential forms on projective bundles and blow-ups.
result Formulas for all cohomologies associated with the complex.
The paper examines the blow-up of Ricci curvatures in conformal metrics.
problem Characterizing the blow-up set of Ricci curvatures in conformal metrics.
method Analyzing the blow-up phenomena of Ricci curvatures on domains close to a limit set of lower dimension.
result Characterization of the blow-up set according to the Yamabe invariant of the manifold.
We show that the blow-up of a generalized Kahler 4-manifold in a nondegenerate complex point admits a generalized Kahler metric. As with the blow-up of complex surfaces, this metric may be chosen to coincide with the original outside a tubular neighbourhood of the exceptional divisor. To accomplish this, we develop a b…
This paper studies a specific blow-up algorithm for sop polynomials and their RLCT.
problem Determining the RLCT of sum-of-products polynomials through blow-up.
method Investigates a specific blow-up algorithm for sop polynomials to resolve their singularities.
result It is possible to resolve the singularities of sop polynomials using a specific blow-up algorithm.
The abstract proves a Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology.
problem Cohomology on complex manifolds, especially non-compact ones.
method Proves a Leray-Hirsch theorem and an explicit blow-up formula.
result Explicit blow-up formula for Dolbeault cohomology on complex manifolds.
Solutions blow up for Yamabe problem on umbilic manifolds with nonzero Weyl tensor.
problem Yamabe problem on manifolds with umbilic boundary
method Building blowing-up solutions
result Solutions blow up for linear perturbation of Yamabe problem
The paper analyzes high-dimensional sphere solutions to the Nirenberg problem with residual mass.
problem The Nirenberg problem on high-dimensional spheres with residual mass.
method Analysis of subcritical approximations and blowing up solutions.
result Comprehensive description of blowing up solutions, including blow-up points and rates.
The Yamabe flow can blow up in infinite time with small perturbations.
problem Understanding the behavior of the Yamabe flow under small perturbations.
method Constructive proof using solutions of the Yamabe problem on the unit sphere as blow-up profiles.
result The Yamabe flow can blow up at multiple points on a Riemannian manifold in infinite time with small perturbations.
The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up …
Study on spinor field equation on spheres, focusing on blow-up analysis.
problem Spinorial Yamabe problem on spheres.
method Variational methods, blow-up analysis.
result Blow-up profile for the spinorial Yamabe type equation on .
Paper analyzes harmonic maps blow-up neck regions.
problem Understanding blow-up regions in harmonic maps.
method Proved refined estimates in neck regions.
result New estimate reveals neck shape and inequality about nullity and index.
Study solutions to metric equations on modified surfaces.
problem Finding constant scalar curvature Kähler metrics on modified surfaces.
method Expanding solutions to extremal metric type equations.
result Developed methods to solve metric equations on modified surfaces.
We prove a gluing formula for Seiberg--Witten invariants which describes in particular the behaviour of the invariant under blow-up and rational blow-down.
Two approaches study the homotopy of blow ups in algebraic and symplectic geometry.
problem Investigate the homotopy of blow ups in algebraic and symplectic geometry.
method Develops fibrewise surgery theory and a purely homotopy theoretic approach.
result Obtained homotopy decompositions of the based loop space on blow ups.
New extremal Poincaré type metrics found via blow-up theorem.
problem Finding new extremal Poincaré type metrics.
method Proved Arezzo-Pacard-Singer blow-up theorem for Poincaré type metrics and applied to new examples.
result Found new examples of extremal Poincaré type metrics with an additional obstruction.
Study on blow-up behavior of sign-changing solutions for Yamabe equation.
problem Blow-up behavior of sign-changing solutions for Yamabe equation.
method Construction of a smooth metric on space forms to prove blow-up at lowest energy level.
result Blow-up occurs at the lowest energy level for sign-changing solutions in dimensions 11 to 24.
Proves inextendibility of weak null singularities from curvature blow-up.
problem Inextendibility of weak null singularities in the context of curvature blow-up.
method Introduces a new strategy to infer -inextendibility from curvature blow-up.
result Expected to contribute to the resolution of strong cosmic censorship conjecture.
Study on solutions of conformal equations, proving bounds and profiles.
problem Analyzing solutions of conformally invariant equations on Euclidean domains.
method Established blow-up profiles and heights of solutions around blow-up points.
result Proved bounds on distances and heights of solutions around blow-up points.
Desingularizes singular foliations with a locally compact groupoid.
problem Handling singularities in foliations.
method Blow-up construction of smooth manifolds and groupoids.
result Locally compact locally Hausdorff groupoid desingularizes singular foliations.
Corrected Monti's blow-up analysis for H-minimizing sets in Heisenberg group.
problem Blow-up analysis of H-minimizing sets in Heisenberg group with corrected partial differential equation.
method Revised Monti's results on blow-ups of H-perimeter minimizing sets in and corrected the partial differential equation for the limit function.
result Corrected the partial differential equation for the limit function of blow-ups in Heisenberg group.
Ancient solutions in Lagrangian flow are classified based on their blow-down.
problem Understanding ancient solutions in Lagrangian mean curvature flow.
method Structural and classification results for ancient solutions, focusing on the almost calibrated case.
result Classification of Type II blow-ups in terms of their blow-down.
The article proves conditions for blow-ups of lcK spaces to remain lcK.
problem Conditions for blow-ups of locally irreducible lcK spaces to remain lcK.
method Proves conditions for blow-ups of lcK spaces to remain lcK.
result Blow-ups of locally irreducible lcK spaces are lcK if and only if the original space is induced gcK.
Formula for Dolbeault cohomology groups on complex manifolds with vector bundles.
problem Calculating Dolbeault cohomology groups on complex manifolds with vector bundles.
method Sheaf-theoretic approach to derive a blow-up formula.
result Uniform presentation of vanishing theorems and blow-up invariance of holomorphic invariants.
Finite-time blow-up in Yang-Mills flow for small energy initial connections.
problem Finite-time blow-up of Yang-Mills flow solutions.
method Analyzing the Yang-Mills flow on Riemannian and Kähler manifolds.
result Finite-time blow-up occurs for small energy initial connections.
The study examines blow-up and global existence of solutions for porous medium equation on curved manifolds.
problem Analyzing blow-up and global existence of solutions for porous medium equation on negatively curved manifolds.
method Examined the porous medium equation with power-type reaction terms on negatively curved Riemannian manifolds.
result For , small data give global solutions; for , large data blow up in infinite time.
Study shows continuity and geometric regularity of Kähler-Ricci flow blow-up limits.
problem Geometric regularity of blow-up limits of the Kähler-Ricci flow.
method Established geometric regularity for Type I blow-up limits based on sequences of Ricci vertices.
result The limiting flow is continuous in time in Gromov-Hausdorff and Gromov- distance.
We show that at generic points blow-ups/tangents of differentiability spaces are still differentiability spaces; this implies that an analytic condition introduced by Keith as an inequality (and later proved to actually be an equality) passes to tangents. As an application, we characterize the -weak gradient on iter…
Study of curvature blow-up in noncompact hypersurfaces using mean curvature flow.
problem Curvature blow-up in mean curvature flow of noncompact hypersurfaces.
method Rotationally symmetric solutions constructed with precise asymptotics.
result Highest curvature concentrates at the tip and blows up at rate .