Related papers: Effective base point freeness on a normal surface
Given a compact Riemannian manifold with boundary, we prove that the space of embedded, which may be improper, free boundary minimal hypersurfaces with uniform area and Morse index upper bound is compact in the sense of smoothly graphical…
It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…
Necessary and/or sufficient conditions are studied for the existence, uniqueness and holonomicity of bases in which on sufficiently general subsets of a differentiable manifold the components of derivations of the tensor algebra over it…
In this article, we prove the boundedness of minimal slopes of adelic line bundles over function fields of characteristic 0. This can be applied to prove the equidistribution of generic and small points with respect to a big and…
An asymptotic formula is established for the number of rational points of bounded height on a non-singular quartic del Pezzo surface with a conic bundle structure.
A projectability result is proved for surfaces of prescribed mean curvature (shortly called $H$-surfaces) spanned in a partially free boundary configuration. Hereby, the $H$-surface is allowed to meet the support surface along its free…
In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the…
On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the…
We give an elementary treatment of the existence of complete Kahler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.
Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.
We employ min-max techniques to show that the unit ball in $\mathbb{R}^3$ contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…
The topology and symmetry group of a free boundary minimal surface in the three-dimensional Euclidean unit ball do not determine the surface uniquely. We provide pairs of non-isometric free boundary minimal surfaces having any sufficiently…
Building on the theory of infinitesimal Newton--Okounkov bodies and previous work of Lazarsfeld--Pareschi--Popa, we present a Reider-type theorem for higher syzygies of ample line bundles on abelian surfaces. As an application of our…
For a given branched covering between closed connected surfaces, there are several easy relations one can establish between the Euler characteristics of the surfaces, their orientability, the total degree, and the local degrees at the…
In the paper we develop a new method of proving non-speciality of a linear system with base fat points in general position. Using this method we show that the Hirschowitz-Harbourne Conjecture holds for systems with base points of equal…
We develop some results on the positivity of direct image bundles in the particular case of a trivial fibration over a one-dimensional base. We also apply the results to study variations of Kahler metrics.
We analyze the point-group symmetries of generic multiband tight-binding models with respect to the transformation properties of the effective interactions. While the vertex functions in the orbital language may transform non-trivially…
We show that the combination of nonnegative 2-intermediate Ricci Curvature and strict positivity of scalar curvature forces rigidity of two-sided free boundary stable minimal hypersurface in a 4-manifold with bounded geometry and weakly…
In this paper we use the theory of mean-stable surfaces (stable minimal surfaces included) to explore the static Einstein-Maxwell space-time. We first prove that the zero set of the lapse function must be contained in the horizon boundary.…