133 papers
This paper establishes that the symmetric algebra of the Bergman space on the unit disk forms a natural algebra over a square-integrable suboperad of holomorphic disk embeddings, which is identified with the affine Heisenberg vertex operator algebra and used to construct metric-dependent invariants for two-dimensional Riemannian manifolds via conformally flat factorization homology.
This paper solves the Snellius-Pothenot problem by determining the number of points in the plane of a fixed triangle that correspond to any given point on the surface defined by the cosines of the angles subtended by the triangle's sides.
This paper investigates rigid-ruling folding motions of curved creases by deriving conditions for the foldability of developable semi-discrete conjugate nets and applying these findings to enable the sequential construction of foldable patterns and characterize the compatibility of planar and constant fold-angle creases.
This paper establishes an asymptotic expansion in inverse powers of time for the correlation functions of isometric extensions of volume-preserving Anosov flows defined on Abelian covers of closed manifolds.
This paper employs the Bahri-Coron barycenter method to establish the existence of a conformal metric with constant higher-order -curvature on specific Riemannian manifolds under a natural positivity condition, notably achieving this result without relying on a positive mass theorem.
This paper extends the definitions of -biharmonic and bi--harmonic maps between Riemannian manifolds and investigates their fundamental properties.
This paper revises Gauss's Lemma by introducing the concept of "metrical distortion" as a non-identity isometry between double tangential and tangential spaces, and concretely defines the exterior differential via covariant gradient transport to incorporate a "differential slip" representing scalar gauge theory, ultimately distinguishing between geodesically radial volume preservation (metrical distortion) and length preservation (exponential mapping) through the example of the 2-sphere.
This paper establishes that Sobolev maps on the product of two Euclidean domains with invertible differentials preserving or swapping the factor spaces are necessarily split when the dimension , a result that fails for and for lower regularity spaces with .
Motivated by non-abelian Hodge theory, this paper formulates a Hodge-theoretic version of Grothendieck's anabelian conjecture by replacing Galois actions with natural -actions, proving an analog of Mochizuki's theorem for smooth projective hyperbolic curves over and extending the result to higher-dimensional ball quotient manifolds.
This paper investigates -twisted almost Hermitian structures, introducing a class of automorphisms called -Codazzi maps due to their relationship with Codazzi tensors, and applies these findings to prove a non-integrability result for the standard nearly Kähler structure on the 6-sphere.
This paper investigates the minimal conditions required to establish Lipschitz and uniform bounds for sequences of bounded rough Riemannian metrics, providing counterexamples to demonstrate the sharpness of these conditions while exploring their underlying geometric intuition.
This paper introduces a graded bracket of forms on multicontact manifolds that satisfies a graded Jacobi identity and Leibniz rules, utilizes multisymplectization to connect these structures to multisymplectic geometry for deriving field equations, and applies these findings to analyze observable evolution, dissipation phenomena, and classical dissipative field theories.
This paper establishes a free probability analogue of Obata's rigidity theorem by proving that under a non-commutative curvature-dimension condition, the saturation of Voiculescu's free Poincaré inequality forces the underlying von Neumann algebra to split off a freely complemented semicircular component, thereby extending classical Gaussian splitting phenomena to the non-commutative setting.
This paper establishes that the optimal rebalancing trajectory for Dynamic Weight Automated Market Makers corresponds to a geodesic under the Fisher-Rao metric (SLERP in Hellinger coordinates), thereby proving that the recursive AM-GM bisection heuristic used in prior work lies exactly on this loss-minimizing path.
This paper establishes that ultralimits of bounded Lipschitz maps extend naturally to Sobolev maps, a result used to prove the stability of Dehn functions under ultraconvergence of pointed length spaces and to provide a simpler proof characterizing spaces of curvature bounded above via isoperimetric inequalities.
This paper establishes universal eigenvalue estimates and derives bounds for the gaps between consecutive eigenvalues for coupled systems of second- and fourth-order elliptic differential equations in divergence form, encompassing operators such as the Lamé, Laplacian, and bi-Laplacian.
This paper establishes that the Bergman kernel of a finite-volume quotient of a Hermitian manifold with bounded geometry is the average of the kernel over the discrete isometry group, and applies this result to Hermitian symmetric spaces to prove the non-vanishing of a broad class of relative Poincaré series, thereby extending previous findings to general locally symmetric spaces of finite volume.
This paper defines and analyzes the asymptotic behavior of the Archimedean height pairing for fiberwise cohomologically trivial differential forms on one-parameter degenerations of Riemann surfaces, utilizing Dai--Yoshikawa's results on small eigenvalues to extend the current-valued pairing of Filip--Tosatti to broader geometric settings.
This paper utilizes family index theory to generalize well-known modular forms to the family setting, thereby deriving new anomaly cancellation formulas for determinant line bundles, index gerbes, eta invariants, and residue Chern forms.
This survey article reviews the theory of twisted dynamical zeta functions of Ruelle and Selberg and explores Fried's conjecture, drawing from a mini-course delivered at the Institut Henri Poincaré.