arXiv research

Geodesic completeness proven for all compact locally symmetric Lorentz manifolds.

In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact manifolds.

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h=1} defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler m…

In this paper, we prove a Liouville theorem for holomorphic functions on a class of complete Gauduchon manifolds. This generalizes a result of Yau for complete Kähler manifolds to the complete non-Kähler case.

Study finds open manifolds without complete metrics with positive scalar curvature.

The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine classification of orientable complete flat 4-manifolds, an algebraic criterion of an affine e…

We prove that every projective special Kähler manifold with \emph{regular boundary behaviour} is complete and defines a family of complete quaternionic Kähler manifolds depending on a parameter $c\ge 0$. We also show that, irrespective of its boundary behaviour, every complete projective special Kähler manifold with \e…

Study describes prosoluble subgroups in 3-manifold groups.

Study shows complete affine manifolds have zero simplicial volume.

We determine all complete projective special real surfaces. By the supergravity r-map, they give rise to complete projective special Kähler manifolds of dimension 6, which are distinguished by the image of their scalar curvature function. By the supergravity c-map, the latter manifolds define in turn complete quaternio…

This paper extends Nevanlinna's unicity theorems to complete Kahler manifolds.

Study on completeness of foliations and null Killing fields in Lorentzian manifolds.

The study provides volume growth estimates for specific types of manifolds.

The paper proves gap theorems for Yang-Mills on manifolds with positive Yamabe.

In studying the Bott-Chern and Aeppli cohomologies for q-complete manifolds, we introduce the class of cohomologically Bott-Chern q-complete manifolds.

Complete minimal surfaces with any genus found in a specific 3-manifold.

We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.

The paper studies curvature changes on manifolds with boundary.

Proves a Liouville-type theorem for p-Laplacian on manifolds.

Localized min-max method proves minimal hypersurface existence.

3-manifolds with toral boundary are uniquely determined by their profinite completions.

Constructs complete Calabi-Yau metrics from smoothed Calabi-Yau intersections.

Let $M$ be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of $M$ is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatur…

For a vector field $X$ on a smooth manifold $M$ there exists a smooth but not necessarily Hausdorff manifold $M_\Bbb R$ and a complete vector field $X_\Bbb R$ on it which is the universal completion of $(M,X)$.

The $L^2$-$\partial\overline\partial$-Lemma is extended to complete Kähler manifolds with a gap in the spectrum.

Generalizes inequality for complete manifolds involving homology classes.

The paper establishes maximum principles and stochastic completeness for pseudo-Hermitian manifolds.

In this paper, we first obtain the sub-Laplacian comparison theorem in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e. Sasakian manifold). Secondly, we derive the sub-gradient estimate for positive pseudoharmonic functions in a complete noncompact pseudohermitian manifold which satisfies the C…

Study on completeness in affine and statistical geometry.

We show the existence of complete negative Kähler-Einstein metric on Stein manifolds with negatively pinched holomorphic sectional curvature. We prove that any Kähler metrics on such manifolds can be deformed to the complete negative Kähler-Einstein metric using the normalized Kähler-Ricci flow.

3-manifolds with similar completions have matching slopes and polynomials.

There has been much recent interest into those properties of a 3-manifold determined by the profinite completion of its fundamental group. In this paper we give readily computable criteria specifying precisely when two orientable graph manifold groups have isomorphic profinite completions. Our results also distinguish …

We study the topology of complete Finsler manifolds admitting convex functions

Study proves rigidity of minimal hypersurfaces in specific manifolds.

Completeness of surface metrics established for Sobolev spaces.

We prove several Liouville-type non-existence theorems for higher order Codazzi tensors and classical Codazzi tensors on complete and compact Riemannian manifolds, in particular. These results will be obtained by using theorems of the connections between the geometry of a complete smooth manifold and the global behavio…

We study transversely Lorentzian foliations on the closed 3-manifolds. We classify them under a completeness hypothesis and we deduce the dual classification of codimension 1 geodesically complete timelike totally geodesic foliations. Besides we provide an example of a Lorentzian foliation on a compact 3-manifold which…

The paper proves optimal estimates and inequalities for spectral functions on certain manifolds.

We prove the uniqueness of solutions of the Ricci flow on complete noncompact manifolds with bounded curvatures using the De Turck approach. As a consequence we obtain a correct proof of the existence of solution of the Ricci harmonic flow on complete noncompact manifolds with bounded curvatures.

The hyperbolization process affects the structure of manifolds.

The paper studies rigidity results for harmonic forms on Kähler manifolds.

Given a sequence of complete Riemannian manifolds $(M_n)$ of the same dimension, we construct a complete Riemannian manifold $M$ such that for all $p \in (1,\infty)$ the $L^p$-norm of the Riesz transform on $M$ dominates the $L^p$-norm of the Riesz transform on $M_n$ for all $n$. Thus we establish the following dichoto…

We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with co-homogeneity one. Complete projective special real manifolds give rise to complete quate…

Negative curvature proven in Sasaki manifold space completion.

The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds was first established by Hamilton \cite{Ha1}. Later on, De Turck \cite{De} gave a simplified proof. In the later of 80's, Shi \cite{Sh1} generalized the local existence result to…

This article presents the further steps of the previously done studies taking into consideration the k-th order extensions of a complex manifold. In the previous studies higher order vertical and complete lifts of structures on the complex manifold were introduced. Presently, k-th extended spaces of a product manifold …

In the present paper we provide a description of complete Calabi-Yau metrics on the canonical bundle of generalized complex flag manifolds. By means of Lie theory we give an explicit description of complete Ricci-flat Kähler metrics obtained through the Calabi ansatz technique. We use this approach to provide several e…

Though Trudinger-Moser inequalities on compact Riemannian manifolds or Euclidean space are well understood, we know little about them on complete noncompact Riemannian manifolds. In this paper, we established respectively necessary condition and sufficient condition under which Trudinger-Moser inequalities hold on comp…