Constructs two types of Eguchi-Hanson metrics with negative scalar curvature.
problem Creating metrics with negative scalar curvature.
method Constructed two types of Eguchi-Hanson metrics.
result Found metrics with negative scalar curvature.
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48 results for “Type I scalar curvature”
Constructs Kähler metrics with constant scalar curvature on blown-up manifolds.
problem Creating Kähler metrics with constant scalar curvature on complex manifolds.
method Blowing up the manifold at points and constructing metrics with Poincaré-type singularities.
result Existence of constant scalar curvature Kähler metrics with Poincaré-type singularities.
Ricci flows with bounded scalar curvature cannot develop Type I singular points.
problem Ricci flows with bounded scalar curvature
method Local singularity analysis
result Scalar curvature must blow up at a Type I rate at each Type I point
The study explores metrics with constant curvature on compact manifolds.
problem Finding Hermitian metrics with constant second scalar curvature on compact manifolds.
method Analyzes Yamabe-type and elliptic equations, derives geometric consequences, and proves existence under specific curvature conditions.
result Under certain curvature conditions, a pluriclosed Gauduchon Hermitian metric has constant second Chern scalar curvature, leading to the existence of Kähler-Einstein metrics.
The paper proves properties of Kähler surfaces with zero scalar curvature.
problem Characterizing Kähler surfaces with zero scalar curvature.
method Analyzing families of generalized Taub-Nut Kähler surfaces and Burn's metric.
result Proves that certain Kähler surfaces are QCH and of specific types.
Paper generalizes scalar curvature theorem to weighted manifolds.
problem Generalizing scalar curvature rigidity theorem to weighted manifolds.
method Proves a refinement of Llarull's theorem for P-scalar curvature.
result Establishes a Llarull type theorem for .
Constructs metrics with negative constant scalar curvature.
problem Negative constant scalar curvature metrics.
method One-parameter family of complete metrics.
result Verifies positive energy conjecture for these metrics.
Constant Scalar Curvature Kähler Metrics on Resolutions of an Orbifold Singularity of Depth 1math.DG
New metrics found on orbifold resolutions with specific curvature.
problem Finding metrics with constant scalar curvature on orbifolds.
method Constructing metrics on resolutions of orbifolds with type I singularities.
result Constant scalar curvature Kähler metrics constructed on resolutions.
Develops Llarull type theorems for 3D and 4D bands with spectral scalar curvature bounds.
problem Bounding scalar curvature and metric on 3D and 4D bands simultaneously.
method Warped -bubble method
result Establishes Llarull type theorems for 3D and 4D bands with spectral scalar curvature bounds.
We show -type inequalities for some end-periodic -manifolds which have positive scalar curvature metrics on the ends. As an application, we construct a new family of closed -manifolds which do not admit positive scalar curvature metrics.
The paper provides obstructions to positive scalar curvature for certain manifolds with group actions.
problem Obstructions to the existence of complete invariant metrics with positive scalar curvature.
method Callias-type index theorem applied to proper actions by locally compact groups.
result Obstructions to positive scalar curvature vanish for certain Lie group actions.
Let D a divisor with simple normal crossings in a Kahler manifold X. The purpose of this short note is to show that the existence of a Poincare type metric with constant scalar curvature in on the complement of D implies for any component of the divisor that the scalar curvature of Poincare type metric outside of D is …
Study finite time singularities in Ricci flow with bounded scalar curvature.
problem Understanding finite time singularities in Ricci flow with bounded scalar curvature.
method Analyzing blow-up sequences of locally Type I singularities.
result Every blow-up sequence of a locally Type I singularity has a specific property.
Study rigidifies Einstein-type manifolds with boundary and constant curvature.
problem Classifying compact Einstein-type manifolds with boundary and constant scalar curvature.
method Applied recent results on gradient Einstein-type manifolds to prove rigidity.
result Rigidity results for compact Einstein-type manifolds with boundary and constant scalar curvature.
The study proves that certain manifolds can have metrics with specific volume growth.
problem Determining if manifolds with positive scalar curvature can have metrics with a given volume growth.
method Using Gromov-Lawson and Grimaldi-Pansu constructions, the study proves the existence of metrics with the desired volume growth on specific manifolds.
result The study positively answers the question for manifolds that are infinite connected sums of closed manifolds with positive scalar curvature.
Study determines scalar curvature invariants for 3-spheres embedded in 4-manifolds.
problem Positive scalar curvature metrics on specific 4-manifolds.
method Relative Bauer-Furuta-type invariant on periodic-end 4-manifolds.
result Obstructions to positive scalar curvature metrics on rational homology .
We carry out a Carlotto-Schoen-type gluing with interpolating scalar curvature on cone-like sets, or deformations thereof, in the category of smooth Riemannian asymptotically Euclidean metrics.
The study classifies specific types of solitons with bounded scalar curvature.
problem Classifying quasi-Yamabe gradient solitons with bounded scalar curvature.
method Analyzing complete, nontrivial solitons with scalar curvature bounded above or below.
result Classification of specific types of solitons with bounded scalar curvature.
In this short note, we use classic computations for Kähler-Ricci flow to achieve scalar curvature bound for minimal manifold of general type.
Introduces a universal Bochner formula for scalar curvature.
problem None explicitly stated; focuses on a new formula.
method Introduces a universal Bochner formula.
result Contains special cases like stability inequality and Schrödinger-Lichnerowicz-type formula.
In this article, we found a connection between Brown-York mass and the first Dirichlet Eigenvalue of a Schrödingier type operator. In particular, we proved a local positive mass type theorem for metrics conformal to the background one with suitable presumptions. As applications, we investigated compactly conformal defo…
New inequalities for austere submanifolds established.
problem Normal scalar curvature inequalities on austere submanifolds.
method Proved sharper DDVV-type inequalities on austere subspaces.
result Achieved equality in normal scalar curvature inequality for a specific austere submanifold.
The paper proves uniformization for specific curvature types on manifolds.
problem Uniformizing fourth order conformal curvature on Riemannian manifolds.
method Proving existence of conformal deformations for specific curvature conditions.
result Existence of conformal deformations for positive Yamabe invariant and total Q-curvature.
New rigidity found for 3D warped product domains.
problem Finding rigidity conditions for warped product domains.
method Developed scalar curvature rigidity for a general class of domains.
result Identified domains satisfying a boundary condition analogous to logarithmic concavity.
This paper is devoted to the existence of contact forms of prescribed Webster scalar curvature on a dimensional CR compact manifold locally conformally CR equivalent to the unit sphere of . Due to Kazdan-Warner type obstructions, conditions on the function to be realized as a We…
The paper extends Ricci flow theory with Type-I scalar curvature bounds, proving entropy convergence and characterizing singular sets.
problem Extending Ricci flow theory with Type-I scalar curvature bounds.
method Type-I rescaling procedure and entropy analysis of conjugate heat kernels.
result Entropy of Ricci flow solutions converges to soliton entropy, characterizing singular sets.
New rigidity theorems for spin fill-ins with non-negative scalar curvature.
problem Mean curvature rigidity for spin fill-ins with non-negative scalar curvature.
method Two spinorial techniques: extending boundary spinors and comparison using index theory.
result New Witten-type integral inequality for the mass of asymptotically Schwarzschild manifolds.
Proves conditions for positive scalar curvature on certain manifolds with conical singularities.
problem Conditions for positive scalar curvature on manifolds with isolated conical singularities.
method Analyzes isolated conical singularities and uses Geroch type results.
result No metric with positive scalar curvature on with isolated conical singularity.
The paper studies automorphisms of generalized Kähler manifolds and their Lie algebras.
problem Understanding the existence or non-existence of generalized Kähler structures with constant scalar curvature.
method Analyzing the Lie algebra of automorphisms of generalized complex manifolds under specific conditions.
result The Lie algebra of automorphisms is reductive if a generalized Kähler structure of symplectic type with constant scalar curvature exists.
We prove that any smooth Riemannian manifold of non-negative scalar curvature and with a strictly mean convex and compact boundary component can be (C^2) extended beyond the component to have non-negative scalar curvature and to enjoy anyone of the following three types of (new) boundary: strictly convex, totally geode…
Generalizes rigidity of scalar curvature for convex domains.
problem Rigidity of scalar curvature for convex domains.
method Harmonic spinors on convex domains with boundary conditions constructed by Brendle.
result Rigidity results on comparison of scalar curvature and scaled mean curvature on the boundary for any convex domain.
Extends Ricci flow theory to Kato-type curvature bounds, proving manifold properties.
problem Extending Ricci flow theory under Kato-type curvature bounds.
method Extends non-collapsed Ricci flow existence theory to Kato-type lower bounds.
result Compact three-dimensional non-collapsed strong Kato limit spaces are homeomorphic to smooth manifolds.
The study finds all possible 3D polytopes in Riemannian 3-manifolds with positive scalar curvature.
problem Understanding the combinatorial types of 3D polytopes in specific Riemannian manifolds.
method Analysis of mean curvature convex Riemannian polyhedra with non-obtuse dihedral angles in positive scalar curvature 3-manifolds.
result Determination of combinatorial types of 3D simple convex polytopes.
Study spherically symmetric Finsler metrics with specific curvature properties.
problem Characterize Finsler metrics with scalar and constant flag curvature.
method Analyze spherically symmetric metrics on symmetric spaces with given curvature properties.
result Provide families of Finsler metrics with scalar and constant flag curvature.
Consider a compact Kähler manifold X with a simple normal crossing divisor D, and define Poincaré type metrics on X\D as Kähler metrics on X\D with cusp singularities along D. We prove that the existence of a constant scalar curvature (resp. an extremal) Poincaré type Kähler metric on X\D implies the existence of a con…
Simplified Obata-Vétois argument for Einstein manifolds with nonnegative scalar curvature.
problem Identifying conditions for closed conformally Einstein manifolds to be Einstein.
method Simplified Obata-Vétois argument, identifying a closed interval containing zero.
result Closed conformally Einstein manifolds with nonnegative scalar curvature are Einstein if they satisfy certain conditions.
Local singularity analysis for Ricci flows with applications to bounded scalar curvature.
problem Understanding the nature of singularities in Ricci flows.
method Local singularity analysis, introducing Type I and Type II singular points, and proving curvature blow-up rates.
result Ricci curvature must blow up at least at a Type I rate near singular points of a Ricci flow.
Let (M,J) be a minimal compact complex surface of Kaehler type. It is shown that the smooth 4-manifold M admits a Riemannian metric of positive scalar curvature iff (M,J) admits a KAEHLER metric of positive scalar curvature. This extends previous results of Witten and Kronheimer.
We study a pointwise inequality for submanifolds in real space forms involving the scalar curvature, the normal scalar curvature and the mean curvature. We translate it into an algebraic problem, allowing us to prove a slightly weaker version of it. We also prove the conjecture for certain types of submanifolds of $\ma…
The paper solves scalar curvature problems under conformal deformation for Riemannian manifolds.
problem Solving scalar curvature problems under conformal deformation for Riemannian manifolds.
method Pointwise conformal deformation, Yamabe equation with Dirichlet boundary conditions.
result Positive, smooth solutions to the Yamabe equation with Dirichlet boundary conditions.
We obtain two types of results on positive scalar curvature metrics for compact spin manifolds that are even dimensional. The first type of result are obstructions to the existence of positive scalar curvature metrics on such manifolds, expressed in terms of end-periodic eta invariants that were defined by Mrowka-Ruber…
The main result of this paper is: Given any constant C, there is such that if a complete, orientable, noncompact odd-dimensional manifold with bounded positive sectional curvature contains a -neck, then the asymptotic scalar curvature ratio is bigger or equal to C. As a application we proved that the…
Developing a singular dimension descent method for positive scalar curvature obstructions
problem Positive scalar curvature obstructions in arbitrary dimensions
method Schoen--Yau type singular dimension descent method
result Proving obstructions to positive scalar curvature on enlargeable manifolds
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 study proves a rigidity theorem for compact manifolds with boundary.
problem Rigidity of compact manifolds with boundary in low dimensions.
method Dimension reduction argument for mean curvature, extending Schoen-Yau's for scalar curvature.
result Sharp spherical radius rigidity and best NNSC fill-in in terms of mean curvature.
Investigates conditions for non-rigidity in extremal metrics involving scalar curvature.
problem Rigidity of extremal metrics involving scalar curvature.
method Analyzes sufficient conditions for non-rigidity and provides examples.
result Provides sufficient conditions for metrics not to be rigid.
New formulas derived for scalar curvature in generalized Ricci flow.
problem Scalar curvature in generalized Ricci flow.
method Derivation of weighted scalar curvature monotonicity formulas and Perelman-type energy/entropy formulas.
result New convex Nash entropies and pseudolocality principles.
Study noncompact manifolds' Chern scalar curvatures, proving existence and multiplicity.
problem Prescribing Chern scalar curvatures on noncompact manifolds.
method Solving a Kazdan-Warner type equation on noncompact non-Kähler manifolds with an analytic condition.
result Established existence results and provided a new proof of multiplicity theorem.