Related papers: Boundedness of n-complements on surfaces

We prove existence and nonexistence results for annular type parametric surfaces with prescribed, almost constant mean curvature, characterized as normal graphs of compact portions of unduloids or nodoids in $\mathbb{R}^{3}$, and whose…

In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.

We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.

We show global existence and boundedness of classical solutions to a virus infection model with chemotaxis in bounded smooth domains of arbitrary dimension and for any sufficiently regular nonnegative initial data and homogeneous Neumann…

We develop a word mechanism applied in knot and link diagrams for the illustration of a diagrammatic property. We also give a necessary condition for determining incompressible and pairwise incompressible surfaces, that are embedded in knot…

Small codimensional embedded manifolds defined byequations of small degree are Fano and covered by lines. They are complete intersections exactly when the variety of lines through a general point is so and has the right codimension. This…

Let X be a Fano manifold of dimension n and index n-3. Kawamata proved the non vanishing of the global sections of the fundamental divisor in the case n=4. Moreover he proved that if Y is a general element of the fundamental system then Y…

Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.

We survey recent results on the boundedness of the moduli functor of stable pairs

Let $(X,B)$ be an $\epsilon$-lc pair of dimension $d$ with a closed point $x\in X$. Birkar and Shokurov conjectured that there is an effective Cartier divisor $H$ passing through $x$ such that $(X,B+tH)$ is lc near $x$, where $t$ is a…

We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.

We study finite $p$-subgroups of birational automorphism groups. By virtue of boundedness theorem of Fano varieties, we prove that there exists a constant $R(n)$ such that a rationally connected variety of dimension $n$ over an…

We give a simple proof that the straightforward generalisation of clique-width to arbitrary structures can be unbounded on structures of bounded tree-width. This can be corrected by allowing fusion of elements.

We study the cones of q-ample divisors on smooth complex varieties. In favourable cases, we identify a part where the closure of this cone and the nef cone have the same boundary. This is especially interesting for Fano (or almost Fano)…

We prove that simply connected H-surfaces with bounded area and free boundary in a domain necessarily concentrate at a critical point of the mean curvature of the boundary of this domain.

We establish global regularity of multilinear Fourier integral operators that are associated to nonlinear wave equations on product of $L^p$ spaces by proving endpoint boundedness on suitable products spaces containing combinations of the…

We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate…

In this paper, we consider mixed sums of generalized polygonal numbers. Specifically, we obtain a finiteness condition for universality of such sums; this means that it suffices to check representability of a finite subset of the positive…

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 prove a combination theorem for PD(n)-pairs.