1033 matching entries · Page 16 of 21
There is a contractible complex three-dimensional domain with a complete Kähler metric whose real sectional curvatures lie between two negative constants, yet it has no bounded holomorphic map to complex three-space with nowhere-vanishing Jacobian and is not biholomorphic to a bounded domain.
There is a closed connected orientable smooth three-manifold that carries a smooth metric without conjugate points but carries no smooth metric of everywhere nonpositive sectional curvature.
A separable reflexive real Banach space has an asymptotically midpoint uniformly convex given norm with averaged midpoint modulus at least √(1+t²/12)−1 for t>0, but admits no equivalent asymptotically uniformly convex norm; depth-k countably branching diamonds have distortion at least √(1+k/12) in it.
For a nonzero real Banach space with the ordinary approximation property, K-convexity holds if and only if both the space and its dual have finite Rademacher cotype, with possibly different exponents.
For every irrational rotation angle θ in (0,1), there is a continuous nonnegative circle weight f with one zero and integral log f equal to negative infinity such that the weighted rotation U f(V) has no nontrivial invariant projection in its associated hyperfinite type II₁ factor.
An explicit separable unital full group C∗-algebra admits no unital embedding into the norm ultrapower B^ω of any nonzero unital nuclear C∗-algebra B for any free ultrafilter ω on the natural numbers.
For the Thorp shuffle on 2^d cards, the full permutation law after 1600d complete shuffles tends to uniform in total variation as d grows, uniformly over initial decks; a support bound requires at least 2d−O(1) shuffles, giving mixing time Θ(d).
For Ising interactions with Haar orthogonal eigenvectors, empirical eigenvalues converging to a compactly supported law, and extreme eigenvalues converging to the support edges, the normalized pressure converges in expectation and almost surely at every fixed positive temperature to the paper’s overlap-hierarchy variational functional.
One stable radial pair potential in three dimensions with a divergent repulsive core and integrable o(r⁻³) tail has canonical free energy at all positive temperatures and densities, with a strict finite jump in its inverse-temperature derivative at one common positive temperature over a nonempty open interval of densities.
For diluted even-arity Ising models in the Panchenko–Talagrand class, finite-system pressure converges to the infimum of the hierarchical cavity trial functional over every finite hierarchy depth and trial law.
A finite Euclidean configuration is Ramsey for monochromatic congruent copies at its original scale exactly when its coordinate field admits the paper’s rational-tensor matrix satisfying the pointwise evaluation identities and identity-matrix product identities; the criterion covers every affine dimension.
For every fixed ε>0, all but o(n) points of any n-point planar set determine at least n^(1−ε) distinct nonzero distances as n grows, uniformly over the set.
For every fixed A>0 and sufficiently large dimension d, a one-pass learner retaining at most Ad² bits between independent exact Gaussian linear measurements needs at least c_A d log(1/ε) measurements to estimate a uniformly random unit vector to angular error ε≤1/10 with success probability at least 2/3.
On positive integral metrics of polynomially bounded diameter, a supplied anchor with distinct accurate proxies for all but logarithmically many comparison clusters and sufficiently small total proxy error supports a polynomial-time k-median recovery algorithm opening at most k facilities and attaining a (1+2/e+ε) factor against those comparison centers with any requested confidence.
There is a countable uniformly discrete metric space whose real Lipschitz-free space has the approximation property but fails every bounded approximation property.
For every proposed constants a,b≥1, some origin-symmetric convex body K in a finite dimension violates Pietsch’s proposed dimension-free covering-entropy comparison with the cube: log N(K,B∞)>b log N(B∞°,a⁻¹K°).
Every real Banach space with Markov type p>1 for some p is superreflexive; with the established converse, nontrivial Markov type characterizes superreflexivity.
There are separable real Banach spaces X and Y with a global bi-Lipschitz bijection but no bounded linear isomorphism between them; X contains an isometric copy of c₀(ℓ₂), while Y contains no bounded linear copy of that space.
Every complex C∗-algebra in which each positive element is properly infinite is strongly purely infinite, satisfying the full positive-element diagonalization property.
There is a bounded self-adjoint tuple X in a von Neumann algebra with faithful normal tracial state for which both microstates and nonmicrostates free entropy are finite yet −∞<χ(X)≤χ*(X)−1/2<∞.
A polynomial-time uniform family of quantum circuits over one fixed finite bounded-arity gate set outputs the complete prime factorization of every integer N≥2 with probability exactly one, using polynomially many gates and qubits in the input bit length.
For every finite two-player game with finite-dimensional entangled value v<1 and arbitrary correlated questions, the maximum probability of winning at least a fraction v+δ of k repetitions decays at least as exp(−κδ¹³k/(1+log(|A||B|))) for one universal κ>0 and 0<δ<1−v.
For every qubit generalized amplitude-damping channel with both parameters in [0,1], unassisted classical capacity equals its one-use Holevo information and an attained one-variable maximum; Holevo information is additive over all repeated uses.
Approximating the electronic Coulomb spectral infimum in three-dimensional continuum space is QMA-hard when positive integer nuclear charges use binary encoding, nuclei have distinct rational positions and electron count is unary; a deterministic polynomial-time reduction produces a promise gap of at least one.
For any pure type system, if every legal expression in every valid context has a terminating β-reduction sequence, then every β-reduction sequence from every such expression terminates, including reductions inside type annotations.
An explicit isomorphism-invariant query on all finite structures in one fixed vocabulary of eight relations is decidable in deterministic polynomial time but is not definable in choiceless polynomial time with counting.
For every d≥3 and β≥0, the free zero-field ferromagnetic Ising law on the infinite d-regular tree is a factor of IID exactly when tanh β≤1/√(d−1), including equality.
On every infinite connected locally finite simple unweighted graph, the free uniform spanning forest is a factor of independent identically distributed vertex labels under one root-free Borel equivariant rule.
For every positive integer n outside {2,4,9}, some irreducible complex representation of Sₙ has a tensor square containing every irreducible complex representation of Sₙ.
A finite-dimensional algebra over F₂(q,H₁,H₂) has a finite-dimensional nonprojective Gorenstein-projective module Z with Extⁱ(Z,Z)=Extⁱ(Z,Λ)=0 for every i>0.
For every C>0, some nonconstant Boolean function on a finite sign cube has the sum of its linear Fourier coefficients greater than C√deg(f), where degree is that of its real multilinear representation.
One explicit 66×66 binary pattern has no polynomial ordered matrix-removal bound: for every c,C>0 there are binary matrices far from avoiding it but with fewer than c ε^C n^132 induced ordered copies.
For random triangle removal from Kₙ, the number of edges left at termination divided by n^(3/2) converges in L² to 1/(2√2).
For every integer d≥3, there are arbitrarily large finite pure connected d-dimensional simplicial complexes with uniformly bounded vertex degree and uniform F₂ coboundary expansion in every degree below d.
For every finite simple graph H with h≥1 edges and at most n vertices, the threshold for G(n,p) to contain an ordinary copy of H is at most C p_E(n,H)(1+log₂ h) for a universal C.
For every natural unit interval graph, its chromatic quasisymmetric function has nonnegative coefficients in the elementary basis over ℕ[q].
A noninvertible C¹ self-map of a compact smooth manifold without boundary has zero topological entropy while its induced action on second real homology has eigenvalue 2.
A C∞ diffeomorphism of the three-torus preserves standard volume and has simple Lebesgue Koopman spectrum on its entire mean-zero L² space.
The trilinear Hilbert transform with fixed slopes 1, 2, and 3 maps three complex L3(R) inputs to L1(R) with a uniform norm bound.
Every smooth connected complex projective Fano variety of dimension six with nef tangent bundle is rational homogeneous.
Every holomorphic one-parameter family of isolated hypersurface singularities in C^3 with constant Milnor number is topologically right-trivial, by a homeomorphism preserving the parameter, origin section, and defining function.
Every smooth connected complex projective contact Fano manifold of complex dimension at least three is contact-isomorphic, with its specified contact distribution, to the adjoint variety of a simple complex Lie algebra.
Every sequence of generalized log canonical flips on a normal globally Weil Q-factorial compact Kähler fourfold terminates when each flip is a projective small diagram with the stated opposite ample signs, rational boundary, and one fixed nef Q-Cartier b-divisor on a projective modification.
For every sufficiently large admissible Hassett discriminant, a very general smooth cubic fourfold in that divisor is irrational although its Kuznetsov component is equivalent to the ordinary derived category of a projective K3 surface.
A smooth projective complex fourfold has large fundamental group but a non-Stein universal cover with no positive-dimensional compact complex-analytic subvarieties.
For every finite quiver, including loops and multiple arrows, and every regular stability character with stable semistable locus and free gauge action, the equivariant cohomology algebra of its Nakajima variety is canonically isomorphic to the coordinate ring of the scheme-theoretic stability-cocharacter fixed locus on the flavor-deformed Coulomb branch.
For a smooth projective complex curve of genus at least two, the perverse and weight filtrations agree on the full rational cohomology of fixed-determinant, trace-free Higgs and character moduli spaces in every composite rank coprime to the degree.
For a projective log canonical threefold pair over an algebraically closed field of characteristic p > 3, if the rational log canonical divisor K_X+B is Q-Cartier, nef, and has numerical dimension one, then it is semiample.
Every continuous open homomorphism between the Galois groups of solvably closed Galois extensions of number fields is induced by a unique equivariant field embedding in the opposite direction, without a kernel restriction.
For every epsilon > 0, infinitely many positive integers n have more than n^(1-epsilon) preimages under Euler’s totient function.
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arXiv · algebra-geometry — last successful metadata check: 21/10/2026, 07:20:46 UTC
arXiv · algorithms-formal — last successful metadata check: 21/10/2026, 07:19:48 UTC
arXiv · analysis — last successful metadata check: 21/10/2026, 07:21:51 UTC
arXiv · combinatorics — last successful metadata check: 21/10/2026, 07:18:49 UTC
arXiv · geometry-topology — last successful metadata check: 21/10/2026, 07:22:23 UTC
arXiv · logic-foundations — last successful metadata check: 21/10/2026, 07:23:04 UTC
arXiv · optimization-information — last successful metadata check: 21/10/2026, 07:23:10 UTC
arXiv · probability-dynamics-physics — last successful metadata check: 21/10/2026, 07:22:36 UTC
arXiv · theoretical-physics — last successful metadata check: 21/10/2026, 07:22:50 UTC
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