Paper refines Talagrand inequality on Euclidean spaces.
problem Improving Talagrand inequality for Euclidean spaces.
method Symmetrization and alternative proof methods.
result Several refined functional inequalities derived.
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48 results for “symmetrization inequalities”
Sharp inequality proven for symmetric functions on a 4D sphere.
problem Proving a sharp Beckner's inequality for axially symmetric functions on .
method Utilized pointwise properties of Gegenbauer polynomials.
result Sharp Beckner's inequality established for axially symmetric functions on .
Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spacesmath.DG
Sharp isoperimetric inequalities for Neumann eigenvalues in symmetric spaces.
problem Finding bounds for eigenvalues of Neumann Laplacian on domains in symmetric spaces.
method Proving sharp inequalities for eigenvalues in compact and noncompact rank-1 symmetric spaces.
result Generalization of previous results for hyperbolic space and symmetric spaces.
Study proves inequality for eigenvalues in symmetric spaces.
problem Proving an inequality for Steklov eigenvalues in symmetric spaces.
method Analyzes eigenvalues on bounded domains in noncompact rank-1 symmetric spaces.
result Extends previous results to non-Euclidean spaces.
Complex and Quaternionic Analogues of Busemann's Random Simplex and Intersection Inequalitiesmath.MG
The paper extends Busemann's inequalities to complex and quaternionic spaces.
problem Extending Busemann's inequalities to complex and quaternionic vector spaces.
method Proof leverages a monotonicity property under symmetrization with respect to complex or quaternionic hyperplanes.
result Standard Steiner symmetrization does not exhibit the monotonicity property in complex or quaternionic spaces.
The paper derives inequalities for submanifolds in quaternionic Kaehler manifolds.
problem Analyzing submanifolds in quaternionic Kaehler manifolds.
method Established Chen's and generalized Casorati curvature inequalities.
result Derived inequalities for submanifolds in quaternionic Kaehler manifolds.
Hineva Inequality for Submanifolds of Real Space Forms with Semi-Symmetric Non-Metric Connectionmath.DG
Paper establishes inequality for submanifolds in real space forms with semi-symmetric non-metric connection.
problem Deriving a sharp lower bound for Ricci curvature of submanifolds.
method Using semi-symmetric non-metric connection, derive a lower bound for Ricci curvature in terms of mean curvature vector and second fundamental form.
result Established Hineva inequality for submanifolds with semi-symmetric non-metric connection.
Paper derives inequalities for submanifolds in a specific geometric space.
problem Chen's inequalities for submanifolds in -contact space form.
method Using generalized semi-symmetric non-metric connections.
result Derives new inequalities for submanifolds.
New inequality shows energy growth and decay in geometric problems.
problem Understanding energy behavior in geometric problems.
method Introduced a symmetric (log-)epiperimetric inequality.
result Energy growth and decay observed in geometric problems.
The article improves Beckner's inequality for axially symmetric functions on the n-dimensional sphere.
problem Improving Beckner's inequality for axially symmetric functions on .
method Uniqueness and existence results for Q-curvature type equations with a Paneitz operator on for axially symmetric functions.
result Improved Beckner's inequality for axially symmetric functions on .
This paper proves a curvature entropy inequality for non-symmetric convex bodies.
problem Proving a curvature entropy inequality for non-symmetric convex bodies.
method Demonstrated the log-Minkowski inequality of curvature entropy for general convex bodies in 2D.
result Equivalence of cone-volume measure uniqueness, log-Minkowski volume inequality, and curvature entropy inequality for general convex bodies in 2D.
Sharp inequalities for star bodies in 2D space.
problem Understanding star bodies in 2D space.
method Sharp inequalities for star bodies in .
result New inequalities and proofs for star bodies.
Sharp inequalities found for orbifold metrics.
problem Bounding systolic ratios on rotationally symmetric orbifolds.
method Analyzing spindle orbifolds and Besse metrics.
result Upper bounds on systolic ratios are attained at Besse metrics.
Paper proves new inequalities for Einstein-Maxwell data sets.
problem Establishing area-charge inequalities for Einstein-Maxwell initial data sets.
method Applying Gromov's μ-bubble technique in a new geometric context.
result Novel rigidity theorems for noncompact Einstein-Maxwell data sets.
Study proves inequalities for eigenvalues of symmetric domains in space forms.
problem Eigenvalue problem for Laplacian on symmetric domains in space forms.
method Symmetry assumptions on domain, proof of inequalities for eigenvalues.
result Proves Szegö-Weinberger type inequalities for first n positive Neumann eigenvalues.
The paper extends geometric inequalities from Euclidean space to Riemannian manifolds.
problem Proving geometric inequalities on smooth oriented Riemannian manifolds.
method Introducing symmetric decreasing rearrangement inequalities and testing their applicability to Riemannian manifolds.
result Smooth co-area formula and re-formulated geometric inequalities on Riemannian manifolds.
In this paper we extend DDVV-type inequalities involving the Frobenius norm of commutators from real symmetric and skew-symmetric matrices to Hermitian and skew-Hermitian matrices.
Proves inequality for special 3D shapes, generalizing to non-symmetric ones.
problem Proving a mathematical inequality for specific 3D shapes.
method Operator theoretic approach combined with spherical function decomposition.
result Generalized inequality for non-symmetric bodies of revolution.
New proof of Wulff-Gage inequality with applications.
problem Proving the Wulff-Gage isoperimetric inequality.
method Provided a new proof of the inequality for origin-symmetric convex bodies.
result Uniqueness of log-Minkowski problem and new proof of log-Minkowski inequality.
Linear inequality found for certain curved spaces.
problem Finding isoperimetric inequalities for curved spaces.
method Extending known result to homogeneous Hadamard manifolds.
result Linear isoperimetric inequality proven for higher-dimensional cycles.
Study of symmetric unions of knots with new inequality and epimorphism results.
problem Understanding the genera of symmetric unions of knots.
method Introduced symmetric unions inspired by earlier work, showed an identity between twisted Alexander polynomials and genera, and established an epimorphism between knot groups.
result Obtained an inequality concerning the genera of symmetric unions and provided a positive answer to an old problem.
Improved Beckner's inequality for axially symmetric functions on S^4.
problem Proving axially symmetric solutions to a constant Q-curvature type equation must be constant.
method Analyzing constant Q-curvature type equations on S^4, using Pohozaev-type identities and bifurcation methods.
result Improved Beckner's inequality for axially symmetric functions on S^4.
The paper proves an inequality for symmetric polynomials under a fixed point measure.
problem An inequality for elementary symmetric polynomials under a fixed point measure of permutations.
method Constructing differential operators to set up a monotone flow.
result The inequality is proven and is sharp.
Paper proves eigenvalue inequality for Hopf-symmetric domains.
problem Eigenvalue inequality for Hopf-symmetric domains in non-compact symmetric spaces.
method Used geometric and spectral analysis on non-compact rank one symmetric spaces.
result Eigenvalue inequality for bounded Hopf-symmetric domains in non-compact symmetric spaces.
Logarithmic Sobolev, Poincaré and Beckner Inequalities on Hyperbolic Spaces and Riemannian Manifoldsmath.AP
Study inequalities on hyperbolic spaces and Riemannian manifolds using symmetrization and heat semigroup.
problem Investigate functional and geometric inequalities on hyperbolic spaces and Riemannian manifolds.
method Employ symmetrization and semigroup approach based on sharp estimates for heat semigroup.
result Developed robust inequalities and methods relying on geometric and isoperimetric properties.
Paper proves curvature estimate for curved spaces.
problem Estimating total curvature of closed hypersurfaces.
method Used non-positively curved symmetric spaces.
result Proved total curvature estimate and isoperimetric inequality.
Proves inequality for tensor fields on curved spaces.
problem Generalizing inequality for tensor fields on curved spaces.
method Alexandrov-Bakelman-Pucci (ABP) method
result Proves Michael-Simon-Sobolev inequality for tensor fields.
In this paper, we will first derive a DDVV-type optimal inequality for real skew-symmetric matrices, then we apply it to establish a Simons-type integral inequality for Riemannian submersions with totally geodesic fibres and Yang-Mills horizontal distributions. In this way, we show phenomenons of duality between Subman…
We use generalised cross--ratios to prove the Ptolemaean inequality and the Theorem of Ptolemaeus in the setting of the boundary of symmetric Riemannian spaces of rank 1 and of negative curvature.
Symmetric log-epiperimetric inequality for harmonic maps with analytic target and applicationsmath.DG
New proof of harmonic map uniqueness with analytic targets.
problem Uniqueness of energy-minimizing harmonic maps with analytic targets.
method Symmetric (log)-epiperimetric inequality for harmonic maps with analytic targets.
result Tangents at infinity of energy-minimizing harmonic maps are unique.
The paper analyzes tensor recovery from symmetric rank-one measurements using information theory.
problem Recovering tensors with low symmetric rank from symmetric rank-one measurements.
method Covering numbers argument, Carbery-Wright inequality, orthogonal polynomials, Fano's inequality.
result Near-optimal sample complexity bounds for log-concave distributions.
The study proves geometric inequalities for static convex domains in static rotationally symmetric spaces.
problem Proving geometric inequalities for static convex domains in static rotationally symmetric spaces.
method Locally constrained curvature flow in a static rotationally symmetric space , proving graphical solutions and static convexity preservation.
result Proves weighted geometric inequalities for static convex domains close to a slice of .
We examine stable solutions of the following symmetric system on a complete, connected, smooth Riemannian manifold without boundary, \begin{equation*} -Δ_g u_i = H_i(u_1,\cdots,u_m) \ \ \text{on} \ \ \mathbb{M}, \end{equation*} when stands for the Laplace-Beltrami operator, $u_i:\mathbb{M}\to \mathbb…
The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or complement of intervals (a result due to Bobkov and Houdré). Then we give a quan…
Researchers prove charged Penrose inequality and positive mass theorem for specific manifold types.
problem Proving inequalities for charged initial data sets with cylindrical ends.
method Doubling argument and application of existing results by Weinstein, Yamada, and Khuri, Weinstein, Yamada.
result Established charged Penrose inequality and positive mass theorem for time symmetric initial data sets with cylindrical ends.
In a symmetric space of noncompact type X = G/K oriented geodesic segments correspond to points in the Euclidean Weyl chamber. We can hence assign vector-valued side-lengths to segments. Our main result is a system of homogeneous linear inequalities describing the restrictions on the side -lengths of closed polygons. T…
We characterize symmetric spaces of non-positive curvature by the equality case of general inequalities between geometric quantities
Moment polytopes in real symplectic geometry II : applications to singular value inequalitiesmath.DG
Study inequalities for singular values of rectangular matrices.
problem Inequalities for singular values of rectangular matrices.
method Study convex cones associated to isotropic representations of symmetric spaces.
result Describe inequalities by cohomological conditions.
Study proposes initial data sets for solving gravitational equations, proving energy estimates.
problem Solving the constraint equations in the evolutionary form.
method Proposes a family of initial data sets, proving Penrose-like energy estimates.
result Established existence of solutions for specific cases.
The paper proposes a conjecture for a symmetric version of Ehrhard's inequality.
problem Formulating a conjecture for the optimal Ehrhard-type inequality for convex symmetric sets.
method Formulating a conjecture and explaining its optimality in terms of Gaussian concavity power.
result Proving certain inequalities for symmetric convex sets, with round k-cylinders as the only equality cases.
Paper proves geodesic ball maximizes second Robin eigenvalue in non-compact symmetric spaces.
problem Maximizing the second Robin eigenvalue in non-compact rank-1 symmetric spaces.
method Quantitative spectral inequality for the second Robin eigenvalue.
result Geodesic ball maximizes the second Robin eigenvalue among domains of the same volume.
Sobolev inequalities involving 2-tensor fields in manifolds with nonnegative sectional curvaturemath.DG
Log Sobolev and Michael Simon inequalities for tensor fields on curved manifolds.
problem Establishing inequalities for tensor fields on curved manifolds.
method Applying the ABP method to symmetric tensor fields on manifolds with nonnegative sectional curvature.
result Log Sobolev and Michael Simon inequalities for tensor fields.
Proves inequalities for tensor fields on submanifolds using ABP method.
problem Proving Michael-Simon inequalities for tensor fields.
method Alexandrov-Bakelman-Pucci (ABP) method
result Proved Michael-Simon inequalities for tensor fields.
In this paper, using functional Steiner symmetrizations, we show that Meyer and Pajor's proof of the Blaschke-Santalo inequality can be extended to the functional setting.
New geometric inequalities for convex bodies derived from Log-Brunn-Minkowski conjecture.
problem Proving geometric inequalities for convex bodies.
method Analyzing semi-norms and symmetric convex bodies, using integral inequalities.
result Characterization and improvement of geometric inequalities involving convex bodies.
In this paper we generalize the known DDVV-type inequalities for real (skew-)symmetric and complex (skew-)Hermitian matrices to arbitrary real, complex and quaternionic matrices. Inspired by the Erdős-Mordell inequality, we establish the DDVV-type inequalities for matrices in the subspaces spanned by a Clifford system …
In this paper, a new approach of defining Steiner symmetrization of coercive convex functions is proposed and some fundamental properties of the new Steiner symmetrization are proved. Further, using the new Steiner symmetrization, we give a different approach to prove a functional version of the Blaschke-Santalo inequa…
Böröczky, Lutwak, Yang and Zhang recently proved the log-Brunn-Minkowski inequality which is stronger than the classical Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane. This paper establishes the log-Brunn-Minkowski, log-Minkowski, -Minkowski and -Brunn-Minkowski inequalities f…