Specialty
A new arXiv preprint presents complementary birational constructions for degree-two marked elliptic surfaces with double fibres, while spelling out where the methods depend on additional assumptions.
Scientific publication5 min read
A mathematical preprint uses Hamiltonian Floer theory to establish a conditional lower bound for periodic solutions in a stochastic particle-field model. The result concerns a theorem and limiting measures, not experimental observations or a full theory of quantum electrodynamics.
Scientific publication5 min read
A theoretical preprint links quantitative K-stability data with the existence of positive scalar curvature Kähler metrics. Under its stated assumptions, a positive threshold corresponds to such a metric, while a threshold above the average scalar curvature corresponds to a unique constant scalar curvature metric. The boundary case requires additional information.
Scientific publication3 min read
A theoretical preprint establishes existence and uniqueness for a Dirichlet problem at infinity involving noncompact convex hypersurfaces in Minkowski space. It also reports conditional global existence and local smooth convergence for a normalized inverse curvature flow, while showing that similar conclusions do not generally carry over to certain quotient flows.
Scientific publication5 min read
An arXiv preprint presents a rigidity theorem for complete shrinking gradient Ricci solitons with constant scalar curvature. If the soliton also satisfies a specified curvature inequality outside a compact region and converges smoothly to R² × Sⁿ⁻², the authors conclude that the entire space is isometric to that product. The proof uses curvature estimates, level-set arguments and geometric-spl คน?
Scientific publication6 min read
A mathematical preprint gives a structural account of hyperbolic-surface entropy, showing that proper-subsurface entropies remain below 1 and that the spectrum has a tightly constrained order.
Scientific publication3 min read
A theorem-based mathematics preprint proposes adding cohomology-driven cap layers to Hamiltonian Floer persistence. In a constructed genus-two example, the refinement distinguishes Hamiltonians that standard Floer summaries cannot separate.
Scientific publication4 min read
A mathematical preprint derives an exact formula for the Hofer–Zehnder capacity of unit disk bundles over ellipsoids. The capacity is determined by the shorter of twice the systole and a shortest Morse-index-3 closed geodesic, while related two-sphere results provide bounds rather than a universal formula.
Scientific publication4 min read
An arXiv preprint shows through algebraic examples and proofs that the Cayley 4-form is not unique in producing a non-degenerate Riemannian metric through Karigiannis’s formula. The work also separates two notions of non-degeneracy and leaves their proposed equivalence unresolved.
Scientific publication5 min read
An arXiv preprint proposes an arithmetic de Rham stack as a common framework for rigid cohomology and related coefficient theories. It states descent, duality, categorical equivalences and arithmetic applications, while leaving the results conditional on their mathematical hypotheses.
Scientific publication5 min read
A geometry preprint presents a proof of Bray’s conjecture, using entropy comparisons, spherical rearrangement and normalized Ricci flow to establish a conditional volume bound for a class of closed Riemannian manifolds.
Scientific publication4 min read
A new arXiv preprint reports that the round disk has the greatest cartographic distortion among convex regions of the same area on the unit sphere. Its result comes from a deterministic geometric proof, not from maps, measurements or human testing.
Scientific publication4 min read
A mathematical preprint constructs K(X) ⊂ K(Y) ⊂ K(Z) with zero inclusion-induced maps on π2, and gives a Lie-ring inclusion where Π2 changes from nonzero to zero.
Scientific publication4 min read
A theoretical preprint develops MU-module and framed sphere-spectrum versions of a Viterbo-type equivalence for the cotangent bundle of a closed smooth manifold. It also explains why passing from sphere spectra to MU cannot generally recover the canonical MU-level construction.
Scientific publication5 min read
A theoretical arXiv preprint connects relative topological Hochschild homology with Frobenius-twisted prismatic structures and works out the surviving rows of a descent spectral sequence for a p-completed example.
Scientific publication3 min read
An arXiv preprint gives a positive answer to a narrowly defined geometric question for three classes of translation surfaces. Its constructions continuously deform polygonal pieces within a fixed stratum and, after unit-area normalization, make the systole—the length of a shortest saddle connection—increase strictly along the path.
Scientific publication5 min read