New examples show negative pseudo-hermitian mass and unattained CR-Sobolev quotient.
problem Negative pseudo-hermitian mass and unattained CR-Sobolev quotient in three-dimensional CR manifolds.
method Examples of compact three-dimensional CR manifolds with positive Webster class (Rossi spheres).
result First geometric context where negative pseudo-hermitian mass and unattained CR-Sobolev quotient arise.
Positive mass theorem and Yamabe equation on CR manifolds
problem Positive mass theorem and Yamabe equation on CR manifolds
method Positive mass theorem and Yamabe equation on CR manifolds
result Positive mass theorem in 3-dimensional CR geometry
The paper introduces new boundary operators and proves higher order CR Sobolev trace inequalities for Siegel domain and complex ball.
problem Establishing higher order CR Sobolev trace inequalities for Siegel domain and complex ball.
method Introducing conformally covariant boundary operators, proving extension theorems, and establishing trace inequalities.
result Generalized CR Sobolev trace inequalities for all γ ∈ (0, n+1) \mathbb{N}.
Improved CR Sobolev inequalities on CR sphere established.
problem Establishing CR Sobolev inequalities on CR sphere.
method Nice commutator identities involving CR intertwining operators.
result Simpler proof of existence and classification of minimizers.
The paper improves CR Sobolev inequalities and classifies minimizers.
problem Higher-order CR Sobolev inequalities on the CR sphere.
method Improvement through vanishing higher order moments of the volume element.
result New direct proof of minimizers' classification and existence of minimizers in C2k(N). Based on uniform CR Sobolev inequality and Moser iteration, this paper investigates the convergence of closed pseudo-Hermitian manifolds. In terms of the subelliptic inequality, the set of closed normalized pseudo-Einstein manifolds with some uniform geometric conditions is compact. Moreover, the set of closed normaliz…
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character analysis.
result Low-regularity spacetimes with unbounded curvature.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character maximizers.
result Low-regularity inextendibility linked to unbounded curvature.
One-Shot Federated Learning learns a global model in one round.
problem Training a global model in federated learning networks.
method Ensemble learning and knowledge aggregation.
result Achieves 51.5% relative gain in AUC over local baselines.
No-regret optimization for time-varying functions using uncertainty injection.
problem Optimizing time-varying functions with no-regret in bandit feedback.
method W-SparQ-GP-UCB, incorporating uncertainty injection and additional queries.
result Achieves no-regret with a vanishing number of additional queries per iteration.
Study option pricing in sideways markets and target zones.
problem Option pricing in sideways markets and target zones.
method Closed-form option pricing formulas for sideways markets and target zones.
result Closed-form option pricing formulas for sideways markets and target zones.
Gaussian processes retain the linear model either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the perspective of the Bayesian posterior, the Gaussian processes which encode the linear model either have probability of nearly…
New RL method designs 3D molecules with improved symmetry.
problem Lack of 3D information in molecular design.
method Symmetry-aware actor-critic architecture using spherical harmonics.
result Improves generalization and molecule quality.
Study examines quotients of affine connection control systems.
problem Existence of quotients preserving mechanical structures.
method Local and global sufficient and necessary conditions for geodesically accessible systems.
result Quotients can be constructed for geodesically accessible systems.
The paper studies hyperbolic quotients of projection complexes and their actions.
problem Understanding the structure and properties of quotients of projection complexes.
method Analyzing the quotient of projection complexes by normal subgroups and studying the resulting actions.
result The quotient complex is δ-hyperbolic under certain conditions, and the quotient group is acylindrically hyperbolic.
The paper introduces pseudo-quotients for algebraic actions and applies them to character varieties.
problem Characterizing algebraic actions and their quotients.
method Introducing pseudo-quotients as a weak version of quotients for algebraic actions, focusing on purely topological properties.
result Pseudo-quotients are unique up to virtual class in characteristic zero and can be used to compute character varieties.
Study non-arithmetic orbifold ball quotients using Jacobian of Bolza curve.
problem Identify and study non-arithmetic orbifold ball quotients.
method Use Jacobian of Bolza curve and birational transformations.
result Obtain orbifold ball quotient surfaces with interesting configurations.
Sharp bounds found on nonabelian quotients of surface braid groups.
problem Finding the smallest nonabelian quotients of surface braid groups.
method Sharp lower bounds and classification of quotients.
result Quotients of minimum order are either symmetric groups or 2-step nilpotent p-groups.
Finite quotients of braid groups have large sizes.
problem Understanding the size of finite quotients of braid groups.
method Derived lower bounds on the size of quotients.
result Lower bounds are superexponential in the number of strands.
Study quotients of curve complex actions by mapping class group.
problem Understanding actions of mapping class group on curve complex quotients.
method Cone off uniformly quasi-convex subspaces to form symmetric curve sets, non-maximal train track sets, and compression body disc sets. Analyze actions of mapping class group on these quotients.
result Actions of mapping class group on quotients are strongly WPD, non-elementary, and have infinite diameter.
Study finds smallest non-trivial quotients of braid groups and commutator subgroups.
problem Identifying smallest non-trivial quotients of braid groups and commutator subgroups.
method Analyzing symmetric and alternating groups for quotients of braid groups and commutator subgroups.
result Proved smallest quotients for specific braid groups and commutator subgroups.
Maximal cubic quotient of braid algebra studied for n ≤ 5.
problem Understanding a maximal quotient of the braid group's algebra with cubic relations.
method Investigating quotients of the group algebra of the braid group with cubic relations.
result Proved isomorphism between the quotient and horizontal chord diagrams for n ≤ 5.
Paper compares total quotient curvature and proves bounds for Einstein metric.
problem Comparing total quotient curvature and proving bounds for Einstein metric.
method Established comparison theorems and proved integral inequalities.
result Background Einstein metric achieves a sharp bound on total quotient curvature.
Researchers show how complex structures vary in symplectic quotients.
problem Understanding how complex structures change in symplectic quotients.
method Two approaches: complex geometry properties and variation of GIT quotients.
result Induced complex structure on symplectic quotients is locally invariant.
Establishes a concavity property for positive Hessian quotient operators.
problem Analyzing positive Hessian quotient operators on Riemannian manifolds.
method Proves a special concavity property and a Jacobi inequality.
result Proves a Jacobi inequality for symmetric tensors.
Paper examines properties of specific solutions to Yamabe flow.
problem Characterizing quotient almost Yamabe solitons.
method Investigates quotient almost Yamabe solitons and presents conditions for their rigidity.
result Sufficient conditions for quotient almost Yamabe solitons to be trivial or isometric with a sphere.
The study shows how quotients of mapping class groups are hierarchically hyperbolic.
problem Understanding the hierarchical hyperbolicity of mapping class groups and their quotients.
method A combinatorial criterion for hierarchical hyperbolicity applied to mapping class groups.
result Quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic.
We solved a conjecture about braid group quotients being alternating groups.
problem Understanding the smallest non-trivial quotients of braid group commutator subgroups.
method Proved the conjecture about alternating groups as quotients, showed minimal quotient maps.
result Proved conjecture about braid group quotients being alternating groups.
Study shows quotient group is infinitely generated.
problem Understanding the structure of homology cobordism groups.
method Proved using Seifert fibered spaces.
result Quotient group is infinitely generated.
Study geodesics on ball quotients to find nonvanishing sections.
problem Finding nonvanishing holomorphic sections on ball quotients.
method Analyzing sequences of pluricanonical bundles associated to closed geodesics.
result Obtain asymptotics of holomorphic sections on ball quotients.
Study on Kohn Laplacian spectrum on sphere quotients.
problem Determining fundamental group from Kohn Laplacian spectrum.
method Weyl-type theorem, CR manifolds, Sobolev estimates.
result Fundamental group can be determined from Kohn Laplacian spectrum in 3D.
Algorithm distinguishes Fuchsian groups with finite quotients.
problem Distinguishing between non-isomorphic Fuchsian groups.
method Develops an algorithm to create group extensions using finite quotients.
result Establishes an upperbound for the order of a distinguishing finite quotient.
Study of Dehn filling quotients in hierarchically hyperbolic groups.
problem Understanding the structure of Dehn filling quotients in specific groups.
method Introduced a construction for cusped spaces of relatively hyperbolic groups and used it to study Dehn-filling-like quotients.
result Infinite hyperbolic quotients of mapping class groups of punctured spheres and braid groups are found.
Reductive quotients preserve klt singularities in algebraic geometry.
problem Preserving klt singularities in quotients of klt singularities.
method Proving that the quotient of a klt type singularity by a reductive group is of klt type.
result The quotient of a klt variety by a reductive group results in a klt variety with a suitable boundary.
The paper studies Lie algebroid and groupoid quotients with forms, applying to Poisson and Dirac structures.
problem Understanding quotients of Lie algebroids and groupoids with compatible differential forms.
method Identifying Lie theoretic conditions for forms to be basic, characterizing induced forms on quotients, and applying results to Poisson and Dirac structures.
result Recovery and generalization of known results on Poisson reduction.
The center of a quotient group of piecewise linear homeomorphisms is trivial.
problem Understanding the structure of a specific group of homeomorphisms.
method Analyzing a quotient of piecewise linear homeomorphisms of the real line.
result The center of the quotient group is trivial.
The study provides interior curvature estimates for convex graphs satisfying a specific quotient equation.
problem Interior curvature estimates for convex graphs.
method Analyzes convex graphs satisfying the quotient equation σn−2σn(λ)=f(X)>0. result Interior curvature estimates for convex graphs.
Quotients of torus endomorphisms have parabolic orbifolds.
problem Understanding the structure of quotients of torus endomorphisms.
method Analyzing the properties of torus endomorphisms and their quotients.
result Every quotient of a torus endomorphism has a parabolic orbifold.
Short note finds a new metric from sphere quotients.
problem Finding metrics from sphere quotients.
method Conformal stereographic projection on sphere quotients.
result Result is a Majumdar-Papapetrou metric.
Study non-existence of complex ball quotients in Torelli locus.
problem Non-existence of totally geodesic complex ball quotients in Torelli locus.
method Analytic techniques.
result Analytic techniques used to study non-existence.
The study finds only spheres shrink self-similarly with quotient curvature speeds.
problem Characterizing self-similar shrinkers for quotient curvature speeds.
method Examined closed hypersurfaces shrinking with quotient curvature speeds.
result Only shrinking spheres are self-similar solutions.
Paper studies Hessian quotient equations in warped product manifolds.
problem Analyzing Hessian quotient equations in warped product manifolds.
method Using standard degree theory and a priori estimates.
result Existence of star-shaped compact hypersurface solutions.
Study proves estimate for Hessian quotient equations on 2D Riemannian manifolds.
problem Problems posed by Delanoë and Urbas related to Hessian quotient equations.
method Maximum principle argument and new test function introduced to prove estimate.
result Unobstructed second order a priori estimate for real Hessian quotient equation in 2D.
Random quotients preserve hyperbolic properties in groups.
problem Preserving hyperbolic properties in random group quotients.
method Independent random walks, spinning families, projection complexes.
result Random quotients of acylindrical and hierarchical hyperbolic groups remain so.
Algorithm optimally estimates linear dynamical systems with active input selection.
problem Estimating parameters of linear dynamical systems efficiently.
method Active learning with adaptive input selection.
result Finite time bound and asymptotic optimality proven.
To a Seifert matrix of a knot K one can associate a matrix w(K) with entries in the rational function field, Q(t). The Murasugi, Milnor, and Levine-Tristram knot signatures, all of which provide bounds on the 4-genus of a knot, are determined by w(K). More generally, the minimal rank of a representative of the class re…
Random quotients of mapping class groups have rigid properties.
problem Rigidity of random quotients of mapping class groups.
method Generalization of Ivanov's theorem and use of hierarchically hyperbolic groups.
result Automorphisms and commensurators of random quotients coincide with the groups themselves.
Quotient spaces of high-dimensional spheres have either zero or large diameter.
problem Understanding the diameter of quotient spaces of high-dimensional spheres.
method Analyzing isometric actions of groups on unit spheres.
result Quotient spaces have diameter zero or larger than a constant.