Proves rigidity for eigenvalue estimate on three-manifolds.
problem Eigenvalue estimate for Kohn Laplacian on three-manifolds.
method Rigidity proof for Lichnerowicz-type estimate.
result Rigidity for eigenvalue estimate on specific three-manifolds.
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48 results for “Lichnerowicz operator”
In this paper, we study some fourth order singular critical equations of Lichnerowicz type involving the Paneitz-Branson operator, and we prove existence and non existence results under given assumptions.
New formula for Lichnerowicz Laplacian on homogeneous spaces.
problem Finding new Einstein metrics on homogeneous spaces.
method Using Casimir operators to derive a new formula for the Lichnerowicz Laplacian.
result Derives many new Einstein metrics stable in the Einstein-Hilbert sense.
Paper extends Poisson-Lichnerowicz cohomology to scalar difference Hamiltonian operators.
problem Classify and understand the deformations of scalar difference Hamiltonian operators.
method Extend Poisson-Lichnerowicz cohomology to difference case, study .
result Triviality of cohomology for with for .
The study examines the geometry of Lichnerowicz Laplacian's kernel on various spaces.
problem Understanding the kernel of the Lichnerowicz Laplacian on different types of spaces.
method Analytical method of Bochner to prove vanishing theorems for null space of Laplace operator.
result Applications to theories of infinitesimal Einstein deformations and stability of Einstein manifolds.
A classical result in differential geometry due to Lichnerowicz [8] is concerned with the decomposition of the square of Dirac operators defined by Clifford connections on a Clifford module \ over a Riemannian manifold . Recently, this formula has been generalized to arbitrary Dirac operators [2]. In this …
Roe C*-algebra for groupoids and generalized Lichnerowicz Vanishing theorem for foliated manifoldsmath.OA
New Roe C*-algebra for non-compact groupoids, leading to foliation Lichnerowicz vanishing.
problem Analyzing elliptic operators on non-compact manifolds with foliations.
method Introducing Roe C*-algebra for groupoids, applying Connes' tangent groupoid method, deriving K-theory.
result Lichnerowicz vanishing theorem for foliations on open manifolds.
The paper proves formulas and theorems for sub-signature operators on manifolds with or without boundaries.
problem Formulating and proving theorems for sub-signature operators on manifolds with boundaries.
method Obtained Lichnerowicz type formulas and proved Kastler-Kalau-Walze type theorems for sub-signature operators.
result Proved Kastler-Kalau-Walze type theorems for sub-signature operators on 4D and 6D compact manifolds with or without boundaries.
The paper describes properties of SpinT(n) and constructs a Dirac operator on Riemannian manifolds.
problem No specific problem stated; focuses on SpinT(n) and Dirac operator construction.
method Described SpinT(n) group, constructed SpinT spinor bundle S, defined covariant derivative and Dirac operator on S, derived Schrodinger-Lichnerowicz-type formula.
result Derived Schrodinger-Lichnerowicz-type formula using the defined operators.
The paper proves formulas and theorems for statistical de Rham Hodge operators on manifolds with boundary.
problem Formulating Lichnerowicz type formulas and Kastler-Kalau-Walze theorems for statistical de Rham Hodge operators.
method Developed Lichnerowicz type formulas and proved Kastler-Kalau-Walze type theorems for statistical de Rham Hodge operators on compact manifolds with boundary.
result Proved Lichnerowicz type formulas and Kastler-Kalau-Walze type theorems for statistical de Rham Hodge operators on compact manifolds with boundary.
The paper proves formulas and theorems for Dirac-Witten operators on manifolds with or without boundaries.
problem Analyzing Dirac-Witten operators on manifolds with boundaries.
method Obtained Lichnerowicz type formulas and proved Kastler-Kalau-Walze type theorems.
result Validated Kastler-Kalau-Walze type theorems for 4D and 6D compact manifolds with or without boundaries.
We construct Dirac operators on foliations by applying the Bismut-Lebeau analytic localization technique to the Connes fibration over a foliation. The Laplacian of the resulting Dirac operators has better lower bound than that obtained by using the usual adiabatic limit arguments on the original foliation. As a consequ…
The paper proves a theorem for a twisted Dirac operator on specific manifolds.
problem Analyzing the Dirac operator with torsion on spin manifolds.
method Develops a Lichnerowicz type formula and proves a Kastler-Kalau-Walze type theorem.
result Proves a Kastler-Kalau-Walze type theorem for the -twist of the Dirac operator with torsion on 4D and 6D almost product Riemannian spin manifolds.
The paper proves a theorem for a twisted Dirac operator on specific manifolds.
problem Analyzing the J-twist of the Dirac operator on spin manifolds.
method Lichnerowicz type formula and Kastler-Kalau-Walze type theorem for the J-twist of the Dirac operator.
result Proves a Kastler-Kalau-Walze type theorem for the J-twist of the Dirac operator on 3D and 4D almost product Riemannian spin manifolds with boundary.
The paper proves formulas and theorems for specific operators on manifolds.
problem Analyzing operators on manifolds and proving theorems.
method Obtained Lichnerowicz type formulas and proved Kastler-Kalau-Walze theorems.
result Proved Kastler-Kalau-Walze type theorems for specific operators.
Study invariant operators and vanishing theorems in CR geometry.
problem Analyzing invariant operators and vanishing theorems in CR geometry.
method Investigates Kohn-Dirac operators and derives CR invariant twistor operators.
result Proves vanishing theorems for harmonic spinors and Kohn-Rossi groups.
The paper studies perturbations of de Rham Hodge operators on manifolds with or without boundaries.
problem Analyzing perturbations of de Rham Hodge operators on manifolds with boundaries.
method Lichnerowicz type formulas and Kastler-Kalau-Walze type theorems for 4D and 6D compact manifolds with or without boundaries.
result Proves Kastler-Kalau-Walze type theorems for perturbations of de Rham Hodge operators on 4D and 6D manifolds with or without boundaries.
Estimates spectral gap for sub-Laplacian on compact manifolds.
problem Bounding the spectral gap of sub-Laplacian on compact manifolds.
method Lichnerowicz estimate adaptation for sub-Laplacian on compact manifolds.
result A bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian.
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are t…
In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and twisted signature operators on 4-dimensional manifolds with (resp. without) boun…
Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivitymath.DG
Investigates uniqueness of conic cscK metrics with cone angles less than π.
problem Uniqueness of conic constant scalar curvature Kähler metrics with cone singularities.
method Introduced a new Hölder space $\cC^{4,\a,\b}$ to study regularities, proved regularity of conic cscK metrics, and established reductivity through careful study of the conic Lichnerowicz operator.
result Any $\cC^{2,\a,\b}$ conic cscK metric is indeed of class $\cC^{4,\a,\b}$.
Study finds rigidity results for manifolds with harmonic Weyl curvature.
problem Characterizing closed manifolds with harmonic Weyl curvature.
method Developed new Bochner-Weitzenböck-Lichnerowicz type formulas for the Weyl tensor.
result Generalized Tachibana's theorem for non-negative curvature operator.
The paper extends Hodge-de Rham and Lichnérowicz Laplacians to double forms and proves vanishing theorems.
problem Extending Laplacians to double forms and proving vanishing theorems.
method Introduced a new product on double forms to establish index-free formulas for curvature terms in Weitzenböck formulas for , , and . Proved vanishing theorems for and on symmetric double forms.
result Vanishing theorems for the Hodge-de Rham Laplacian and on symmetric double forms.
New findings on curvature and null spaces of Laplacians.
problem Relationship between sectional curvature and Laplacian null spaces.
method Analysis of curvature operators and Laplacians on Riemannian manifolds.
result Curvature operator's positivity implies sectional curvature positivity.
Modified Novikov Operators and the Kastler-Kalau-Walze type theorem for manifolds with boundarymath.DG
The paper proves formulas and theorems for modified Novikov operators on manifolds with boundary.
problem Analyzing modified Novikov operators on manifolds with boundary.
method Developed Lichnerowicz type formulas and proved Kastler-Kalau-Walze type theorems.
result Proved Kastler-Kalau-Walze type theorems for modified Novikov operators on compact manifolds with boundary.
Paper studies eigenvalue bounds for complex curves on Kähler surfaces.
problem Investigates eigenvalue bounds for complex curves on Kähler surfaces.
method Analyzes second variation of a conformally invariant Willmore-type functional to derive bounds.
result Derives lower bound for Kähler surfaces, with equality for low genus curves.
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric…
In this paper, we study Lichnerowicz type estimate for eigenvalues of drifting Laplacian operator and L1 and L2 energy for drifting heat equation on closed manifolds with weighted measure. In some sense, this study is about the eigenvalue estimate on Ricci solitons.
New proof shows solutions to Lichnerowicz equation exist.
problem Existence of solutions to the Lichnerowicz equation in general relativity.
method A new proof approach.
result Existence and uniqueness of solutions proven.
The motivation of this paper is to study a second order elliptic operator which appears naturally in Riemannian geometry, for instance in the study of hypersurfaces with constant -mean curvature. We prove a generalized Bochner-type formula for such a kind of operators and as applications we obtain some sharp estimat…
This paper studies geodesics and uniqueness of cscK cone metrics.
problem Uniqueness of constant scalar curvature Kahler cone metrics.
method Introduction of weighted function spaces, construction of cone geodesics, detailed asymptotic analysis of cscK cone metrics, linear theory for Lichnerowicz operator.
result The cscK cone metric is unique up to automorphisms.
New eigenvalue bounds for 3-Sasaki metrics improve previous estimates.
problem Estimating eigenvalues for 3-Sasaki metrics.
method Improved Lichnerowicz-Obata type estimates for scalar sub-Laplacian.
result Lower bounds for the first non-zero eigenvalue of 3-Sasaki metrics.
Lichnerowicz-Jacobi cohomology and homology of Jacobi manifolds are reviewed. We present both in a unified approach using the representation of the Lie algebra of functions on itself by means of the hamiltonian vector fields. The use of the associated Lie algebroid allows to prove that the Lichnerowicz-Jacobi cohomolog…
Proves existence and uniqueness of solutions to Lichnerowicz-type equations on manifolds.
problem Existence and uniqueness of positive solutions to Lichnerowicz-type equations on complete manifolds.
method Proves existence and uniqueness via spectral assumptions and a priori bounds.
result Proves existence and uniqueness of solutions to Lichnerowicz-type equations on manifolds.
In this paper we provide a detailed proof of the second variation formula, essentially due to Richard Hamilton, Tom Ilmanen and the first author, for Perelman's -entropy. In particular, we correct an error in the stability operator stated in Theorem 6.3 of [2]. Moreover, we obtain a necessary condition for linearly …
Paper finds a graph Steklov eigenvalue estimate with rigidity results.
problem Estimating Steklov eigenvalues on graphs.
method Lichnerowicz-type estimate for the first Steklov eigenvalues.
result Rigidity results for the Steklov eigenvalues on graphs.
We discuss a peculiar interplay between the representation theory of the holonomy group of a Riemannian manifold, the Weitzenboeck formula for the Hodge-Laplace operator on forms and the Lichnerowicz formula for twisted Dirac operators. For quaternionic Kaehler manifolds this leads to simple proofs of eigenvalue estima…
New estimates show all stable Einstein manifolds are linear stable with respect to Perelman's ν-entropy.
problem Estimating the smallest eigenvalue of Laplace-Beltrami operator for stable Einstein manifolds.
method Estimating the smallest positive eigenvalue of the Laplace-Beltrami operator for standard Einstein manifolds and proving for all but 7 exceptions.
result All stable Einstein manifolds found by Schwahn are linear stable with respect to Perelman's ν-entropy.
We construct a series of conformally invariant differential operators acting on weighted trace-free symmetric 2-tensors by a method similar to Graham-Jenne-Mason-Sparling's. For compact conformal manifolds of dimension even and greater than or equal to four with vanishing ambient obstruction tensor, one of these operat…
We establish a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions, when the action group is unimodular.
Study describes bifurcations and solutions of a specific equation on a particular manifold.
problem Analyzing bifurcations and solutions of the vacuum Lichnerowicz equation.
method Exhaustive description of bifurcations and solutions on with invariant seed data.
result Description of CMC slicings of Schwarzschild-de Sitter and Nariai solutions.
Proves existence of solution to Lichnerowicz equation on non-CMC manifolds.
problem Existence of positive solution to Lichnerowicz equation on non-CMC closed manifolds with supercritical terms.
method Employed a fixed-point argument involving sub- and supersolutions, with conditions on coefficients to prevent classical solutions.
result Proves existence of a positive and essentially bounded solution.
Proves Laplacian and Lichnerowicz Laplacian are sectorial in weighted Hölder spaces.
problem Analyzing sectoriality of Laplacian and Lichnerowicz Laplacian on asymptotically hyperbolic spaces.
method Proves sectoriality in weighted Hölder spaces using asymptotically hyperbolic metrics.
result Analytic semigroups apply, yielding well-posedness results for parabolic evolution equations.
New gauge preserves Einstein metrics' interactions, proving rigidity on negatively curved manifolds.
problem Stability and deformation theory of Einstein metrics.
method Introduces Chen-Nagano gauge condition, linking Lichnerowicz Laplacian to shifted scalar operator.
result Chen-Nagano gauge collapses to classical transverse-traceless gauge under spectral pinching assumptions.
Formula for Lichnerowicz Laplacian on invariant metrics, deducing stability of Einstein manifolds.
problem Stability of Einstein manifolds in homogeneous spaces.
method Formula for Lichnerowicz Laplacian, computation of spectra, analysis of scalar curvature.
result Deduction of -stability and critical point types of Einstein metrics.
Lichnerowicz-type equations with sign-changing nonlinearities on complete manifolds with boundarymath.AP
Proves existence of positive solutions to equations on manifolds with boundary.
problem Solving Lichnerowicz-type equations on manifolds with boundary.
method Existence theorem for positive solutions on complete manifolds with boundary and nonlinear Neumann conditions.
result Proves existence of positive solutions to Lichnerowicz-type equations.
The original version of the paper claimed to disprove the pseudo-Riemannian Lichnerowicz conjecture of D'Ambra and Gromov. However, the argument contains a crucial sign error in the lines following equation (8).
We prove the Finsler analog of the conformal Lichnerowicz-Obata conjecture showing that a complete and essential conformal vector field on a non-Riemannian Finsler manifold is a homothetic vector field of a Minkowski metric.