New solitons found for G-Laplacian flow on Lie groups.
problem Existence of solitons for G-Laplacian flow.
method Existence proof for expanding and steady solitons.
result First example of non-extremally Ricci pinched steady soliton.
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48 results for “steady Laplacian solitons”
Study of solitons in Laplacian flow on 7-manifolds.
problem Understanding finite-time singularities of Laplacian flow on G_2-structures.
method Systematic study of cohomogeneity-one solitons with Sp(2) and SU(3) symmetry groups.
result Existence and classification of smoothly-closing solitons, including complete and incomplete solutions.
We give the first examples of closed Laplacian solitons which are shrinking, and in particular produce closed Laplacian flow solutions with a finite-time singularity. Extremally Ricci pinched G2-structures (introduced by Bryant) which are steady Laplacian solitons have also been found. All the examples are left-invaria…
Study shows instability of Kähler Ricci solitons and stability of orbifold singularities.
problem Linear stability and instability of Kähler Ricci solitons.
method Extending the approach of \cite{chi04} and \cite{hm11}, via recent work \cite{cm21} on gradient shrinking Ricci solitons.
result Linear instability of the BCCD shrinking soliton and stability of orbifold singularities of Kähler solitons.
New G2-structures found on Lie groups with strong structural conditions.
problem Existence and structure of extremally Ricci pinched G2-structures on Lie groups.
method Strong structural conditions on Lie algebra, deformation and rigidity studies.
result Three new examples of extremally Ricci pinched G2-structures, all steady Laplacian solitons.
In this paper, it is shown that (with no additional assumptions) on a compact 7-dimensional manifold which admits a -structure soliton solutions to the Laplacian flow of R. Bryant can only be shrinking or steady. We also show that the space of symmetries (vector fields that annihilate via the Lie derivative) of a …
Study on steady solitons' curvature behavior near infinity.
problem Curvature estimate of steady solitons near infinity.
method Investigation of asymptotic curvature properties.
result Asymptotic curvature estimate for steady solitons.
Investigates noncompact warped product Ricci solitons, proving nonexistence results.
problem Proving nonexistence results for noncompact warped product Ricci solitons.
method Proves nonexistence results using pde estimates and properties of the first eigenvalue of a weighted Laplacian.
result Nonexistence theorem for shrinking Ricci solitons.
The study classifies steady Ricci solitons based on geometric conditions.
problem Characterizing steady Ricci solitons under specific geometric constraints.
method Analyzing geometric conditions and applying them to classify solitons.
result Steady Ricci solitons are classified into specific types based on given conditions.
Unique steady and expanding solitons with spherical links identified.
problem Characterizing steady and expanding Ricci solitons with specific asymptotic symmetries.
method Symmetry principle applied to asymptotically cylindrical and conical GRSs, proving uniqueness for Bryant solitons.
result Bryant steady and expanding solitons are the unique asymptotically cylindrical and conical GRSs with spherical links under certain conditions.
Researchers prove isoperimetric inequality in specific steady Ricci solitons.
problem Proving the isoperimetric inequality in steady Ricci solitons.
method Utilized Guan-Li-Wang's result on warped product metrics and analyzed the soliton structure.
result Proved the isoperimetric inequality in the cigar and Bryant steady solitons.
In this paper we study potential function of gradient steady Ricci solitons. We prove that infimum of potential function decays linearly; in particular, potential function of rectifiable gradient steady Ricci solitons decays linearly. As a consequence, we show that a gradient steady Ricci soliton with bounded potential…
The paper classifies special hypersurfaces in space forms.
problem Investigating gradient Yamabe solitons in space forms.
method Using the weak Omori-Yau principle for the drifted Laplacian.
result Gradient Yamabe solitons are fully classified under certain conditions.
New classification of gradient steady Ricci solitons with vanishing D-tensor.
problem Classifying gradient steady Ricci solitons with specific properties.
method Extending Cao-Chen's work on Bach-flat gradient Ricci solitons, proving properties for -flat solitons.
result Any -dimensional complete noncompact gradient steady Ricci soliton with vanishing -tensor is either Ricci-flat or isometric to the Bryant soliton.
Paper proves volume growth estimate for steady gradient Ricci solitons.
problem Estimating the volume growth of steady gradient Ricci solitons.
method Proved a volume growth estimate using Nash entropy.
result Volume growth rate is no smaller than $r^{ rac{n+1}{2}}$.
3D steady gradient Ricci solitons are all O(2)-symmetric.
problem Characterizing 3D steady gradient Ricci solitons.
method Analyzing asymptotic behavior and using O(2) symmetry.
result All 3D steady gradient Ricci solitons are O(2)-symmetric.
In this paper, we give a description for steady Ricci solitons with a linear decay of sectional curvature. In particular, we classify all 3-dimensional steady Ricci solitons and 4-dimensional -noncollpased steady Ricci solitons with nonnegative sectional curvature under the linear curvature decay.
Study steady gradient Ricci solitons with cylindrical tangent flows at infinity.
problem Characterize the geometry of steady gradient Ricci solitons at infinity.
method Analyze the rescaled limits of finite-time singular solutions of the Ricci flow.
result Classify the tangent flows at infinity of 4-dimensional steady soliton singularity models.
Unique soliton found on resolved cones.
problem Existence of Kähler-Ricci solitons on Calabi-Yau cones.
method Equivariant crepant resolutions and steady gradient Kähler-Ricci solitons.
result Unique complete steady gradient Kähler-Ricci soliton found.
Study 4D steady gradient Ricci solitons reducing to 3D manifolds.
problem Understanding 4D steady gradient Ricci solitons that reduce to 3D.
method Analyzing asymptotic geometry and curvature properties.
result 4D solitons either reduce to spherical space forms or the 3D Bryant soliton.
In this paper we prove that any -dimensional () complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant sol…
This research shows that steady solitons in higher dimensions always reduce at infinity.
problem Characterizing steady solitons with nonnegative sectional curvature in higher dimensions.
method Dimension reduction analysis and tangent flow classification.
result Steady solitons in higher dimensions always reduce at infinity.
In this paper, we classify n-dimensional (n>2) complete noncompact locally conformally flat gradient steady solitons. In particular, we prove that a complete noncompact non-flat conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton.
Study on scalar curvature decay in four-dimensional steady solitons.
problem Behavior of scalar curvature at infinity on four-dimensional steady solitons.
method Analysis of scalar curvature decay rate and asymptotic cone properties.
result Linear scalar curvature decay away from edges, stronger inequality if scalar curvature vanishes at infinity.
A note on the classification of four-dimensional gradient steady and expanding Ricci solitonsmath.DG
Study classifies 4D Ricci solitons with specific curvature conditions.
problem Classifying 4D gradient steady and expanding Ricci solitons with given curvature properties.
method Asymptotically cylindrical and conical assumptions; half-harmonic and half-nonnegative isotropic curvature conditions.
result Partial classification of 4D gradient expanding Ricci solitons with half-nonnegative isotropic curvature.
Study of 4D Ricci solitons with symmetry, finding precise geometric asymptotics.
problem Classifying 4D gradient steady Ricci solitons and understanding their geometric properties.
method Analysis of 4D gradient steady Ricci solitons with O(3)-symmetry under a weak curvature decay condition.
result Find precise geometric asymptotics similar to 3D compact κ-solutions.
Classification of 3-dimensional complete rectifiable steady and expanding gradient Ricci solitonsmath.DG
3D solitons classified into specific types.
problem Classifying 3D steady and expanding gradient Ricci solitons.
method Analyzing rectifiable potential functions and curvature conditions.
result 3D solitons are isometric to specific known forms.
The paper studies steady solitons with curvature decay and proves their smoothness.
problem Analyzing the properties of steady solitons with curvature decay.
method Bootstrap regularity in harmonic coordinates using the soliton equation.
result Steady gradient Ricci solitons are asymptotically cylindrical under certain curvature decay conditions.
Introduces a new length functional for Ricci flow to detect steady solitons.
problem Detecting steady solitons in Ricci flow.
method Develops a modified length functional and shows it satisfies differential inequalities.
result The length functional generates a distance function that saturates on steady soliton manifolds.
In this paper, we analyze the asymptotic behavior of -noncollapsed and positively curved steady Ricci solitons and prove that any -dimensional -noncollapsed steady Kähler-Ricci soliton with non-negative sectional curvature must be flat.
The two-loop renormalization group flow is studied via the induced bracket flow on 3D unimodular Lie groups. A number of steady solitons are found. Some of these steady solitons come from maximally symmetric metrics that are steady, shrinking, or expanding solitons under Ricci flow, while others are not obviously relat…
Researchers found infinitely many non-collapsed steady Ricci solitons on complex line bundles.
problem Finding steady Ricci solitons on complex line bundles.
method Constructed a continuous 3-parameter family of non-shrinking Ricci solitons.
result Includes infinitely many asymptotically paraboloidal steady Ricci solitons.
New steady solitons found with SO(3) symmetry.
problem Finding steady solitons with specific symmetries.
method Proved existence of a family of solitons with SO(3) symmetry.
result Existence of a one-parameter family of solitons.
The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.
problem Analyzing noncompact steady gradient Ricci solitons with nonnegative curvature operator.
method Examining the asymptotic behavior of noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative curvature operator away from a compact set.
result 4D noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature must be a Bryant Ricci soliton up to scaling.
Study on curvature decay in steady Ricci solitons, proving dichotomy.
problem Curvature decay in steady Ricci solitons.
method Established a dichotomy for curvature decay in specific types of solitons.
result Proved a dichotomy on curvature decay for certain steady Ricci solitons.
New Kähler solitons found that are not -invariant.
problem Whether every steady gradient Kähler-Ricci soliton of positive curvature on is -invariant.
method Constructing a family of -invariant, but not -invariant, steady gradient Kähler-Ricci solitons.
result Found a family of complete steady gradient Kähler-Ricci solitons with strictly positive curvature operator on for .
The paper examines gradient Ricci solitons on orbifolds and proves their rigidity properties.
problem The rigidity of positively curved gradient Ricci solitons on orbifolds.
method Analyzes scalar curvature, uses nonnegative curvature operator, κ-noncollapsed condition, and asymptotic quotient cylindrical properties.
result Steady gradient Ricci solitons on orbifolds with positive curvature are rigid and must be quotients of the Bryant soliton.
Study proves rigidity of certain gradient steady Ricci solitons with harmonic Weyl curvature.
problem Investigating rigidity of specific gradient steady Ricci solitons.
method Proving rigidity for -dimensional () complete noncompact gradient steady Ricci solitons with harmonic Weyl tensor.
result Proves that such solitons are either Ricci flat or isometric to the Bryant soliton up to scaling.
New decay estimates for scalar curvature of steady gradient Ricci solitons.
problem Understanding scalar curvature behavior in steady gradient Ricci solitons.
method Using μ-bubbles introduced by Gromov.
result Provide new decay estimates for scalar curvatures.
The only known example of collapsed three-dimensional complete gradient steady Ricci solitons so far is the 3D cigar soliton , the product of Hamilton's cigar soliton and the real line with the product metric. R. Hamilton has conjectured that there should exist a family of colla…
Survey paper analyzes curvature estimates for 4D gradient Ricci solitons.
problem Analyzing curvature estimates for different types of 4D gradient Ricci solitons.
method Comparison and new estimates provided for 4D gradient steady Ricci solitons.
result Sharp curvature estimate for gradient steady Ricci solitons with positive Ricci curvature.
Researchers discover a new family of 3D solitons that are flying wings.
problem Verifying a conjecture about 3D steady gradient Ricci solitons.
method Analyzing a family of 3D flying wing solitons and proving properties of these solitons.
result 3D flying wing solitons are non-collapsed and have non-zero scalar curvature at infinity.
Paper shows triviality criterion for certain Ricci solitons.
problem Identifying trivial non-steady gradient Ricci solitons.
method Analyzes scalar curvature and its relation to triviality.
result Triviality of solitons depends on scalar curvature equality.
The linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equationmath.DG
We show that the linear trace Harnack quadratic on a steady gradient Ricci soliton satisfies the heat equation. Similar result holds for shrinkers. We also present an interpolation between Perelman's and Cao--Hamilton's Harnacks on a steady soliton.
New steady Kähler-Ricci solitons found on orbifolds.
problem Constructing steady Kähler-Ricci solitons on orbifolds.
method Using asymptotically cylindrical structures and orbifold actions.
result Found new examples of gradient steady Kähler-Ricci solitons converging to a Ricci-flat cylinder.
Study on Kähler-Ricci solitons on toric manifolds, proving rigidity.
problem Characterizing gradient steady Kähler-Ricci solitons on toric manifolds.
method Analyzing orbit space structure and using Bakry-Émery tensor.
result Proves rigidity of solitons on complete toric manifolds.
New steady gradient Ricci solitons found with specific symmetry.
problem Finding new steady gradient Ricci solitons with positive curvature.
method Utilized a procedure by Lai to construct examples with symmetry.
result Found new examples of steady gradient Ricci solitons with symmetry in dimensions .
On the fundamental group of steady gradient Ricci solitons with nonnegative sectional curvaturemath.DG
Paper studies fundamental groups of certain Ricci solitons.
problem Understanding fundamental groups of specific Ricci solitons.
method Analyzes properties of complete steady gradient Ricci solitons with nonnegative sectional curvature.
result Fundamental groups of these solitons are either trivial or infinite.