Related papers: Effective base point freeness on a normal surface

We prove the multiplicity one theorem for min-max free boundary minimal hypersurfaces in compact manifolds with boundary of dimension between 3 and 7 for generic metrics. To approach this, we develop existence and regularity theory for free…

The surface impedance approach to the description of the thermal Casimir effect in the case of real metals is elaborated starting from the free energy of oscillators. The Lifshitz formula expressed in terms of the dielectric permittivity…

An elementary result in point-set topology is used, with knowledge of the mod $2$ cohomology of real projective spaces, to establish classical results of Lebesgue and Knaster-Kuratowski-Mazurkiewicz, as well as the topological central point…

In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We…

We present a systematic treatment of line bundle geometry and Jacobi manifolds with an application to geometric mechanics that has not been noted in the literature. We precisely identify categories that generalise the ordinary categories of…

Under the assumption that data lie on a compact (unknown) manifold without boundary, we derive finite sample bounds for kernel smoothing and its (first and second) derivatives, and we establish asymptotic normality through Berry-Esseen type…

We survey several applications of fixed point theorems in the theory of invariant subspaces. The general idea is that a fixed point theorem applied to a suitable map yields the existence of invariant subspaces for an operator on a Banach…

In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free…

This is the sequel of the recent work (Du, Huang, Pu, Commun. Math. Phys, 2023, doi: 10.1007/s00220-023-04651-7) on axially symmetric gravity water waves with general vorticities, which has investigated the singular wave profile of the free…

We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which the real locus is connected and the intermediate Jacobian…

We investigate a variational problem in the Lorentz-Minkowski space $\l^3$ whose critical points are spacelike surfaces with constant mean curvature and making constant contact angle with a given support surface along its common boundary.…

For almost all Riemannian metrics (in the $C^\infty$ Baire sense) on a compact manifold with boundary $(M^{n+1},\partial M)$, $3\leq (n + 1)\leq 7$, we prove that, for any open subset $V$ of $\partial M$, there exists a compact, properly…

In this paper, we give a relationship between the eigenvalues of the Hodge Laplacian and the eigenvalues of the Jacobi operator for a free boundary minimal hypersurface of a Euclidean convex body. We then use this relationship to obtain new…

We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of…

We establish the Hasse principle for $100\%$ of conic bundles over $\mathbb{P}^1_{\mathbb{Q}}$.

For several embedded surfaces with zero self-intersection number in 4-manifolds, we show that an adjunction-type genus bound holds for at least one of the surfaces under certain conditions. For example, we derive certain adjunction…

We prove an effective upper bound on the number of effective sections of a hermitian line bundle over an arithmetic surface. It is an effective version of the arithmetic Hilbert--Samuel formula in the nef case. As a consequence, we obtain…

Motivated by the theory of quantum waveguides, we investigate the spectrum of the Laplacian, subject to Dirichlet boundary conditions, in a curved strip of constant width that is defined as a tubular neighbourhood of an infinite curve in a…

We define a 2-normal surface to be one which intersects every 3-simplex of a triangulated 3-manifold in normal triangles and quadrilaterals, with one or two exceptions. The possible exceptions are a pair of octagons, a pair of unknotted…

A conjecture for higher order separation on generic rational surfaces with some new results about standard divisors.