arXiv research

Paper proves equivariant Fried conjecture for specific flows.

We study Lie foliations on compact manifolds, in case the Lie group is compact. Our main results improve Tischler classical result on the existence of fibration and, as an application, we study the case the manifold has an amenable fundamental group.

Geodesic completeness proven for all compact locally symmetric Lorentz manifolds.

The paper explores knot invariants using quantum dilogarithm representations and compares them to compact cases.

We introduce a notion of relative isospectrality for surfaces with boundary having possibly non-compact ends either conformally compact or asymptotic to cusps. We obtain a compactness result for such families via a conformal surgery that allows us to reduce to the case of surfaces hyperbolic near infinity recently stud…

Projective geometry aids in analyzing fields near compact manifolds.

We investigate different concentration-compactness phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in $R^{2m}$, then that of a closed manifold and, finally, the particular case of the sphere $S^{2m}$. In all cases we allow the sign of the Q-curvature to vary, …

We consider Lorentzian manifolds with parallel light-like vector field V. Being parallel and light-like, the orthogonal complement of V induces a codimension one foliation. Assuming compactness of the leaves and non-negative Ricci curvature on the leaves it is known that the first Betti number is bounded by the dimensi…

Study on invariant anti-quasi-Sasakian structures on compact manifolds.

Study sharp decay of capacity for subharmonic functions on compact Hermitian manifolds.

Compact capillary hypersurfaces with specific curvatures are proven.

Extends soliton theory to non-compact cases.

In this two papers we deal with the relative homotopy Dirichlet problem for p-harmonic maps from compact manifolds with boundary to manifolds of non-positive sectional curvature. Notably, we give a complete solution to the problem in case the target manifold is either compact and a new proof in case it is rotationally …

Let $Σ$ be a $C^3$ compact symmetric convex hypersurface in $\mathbf{R}^{8}$. For some special cases, we prove that when $Σ$ carries exactly four geometrically distinct closed characteristics, then all of them must be symmetric.

Novel approach ensures stability of compact schemes for variable PDEs.

Bonahon's method for compactifying Teichmüller space extended to non-compact surfaces.

We verify a conjecture for compact balanced threefolds and LCK manifolds with constant holomorphic sectional curvature.

Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function is calculated via zeta-function regularization with special attention to its mo…

Compact Einstein manifolds of low dimensions are studied based on Lie group actions.

Study G-H limits of surfaces with boundary, focusing on same Euler characteristic.

The study characterizes compact homogeneous manifolds with Bismut parallel torsion.

Condition for Anosov flows on non-compact manifolds without conjugate points.

Analytic torsion defined for non-compact Lie groups and discrete subgroups.

This paper shows stable mappings are never dense on non-compact manifolds.

Compact automorphism group of a topological parallelism in real projective 3-space proved.

Defines geometric quantization for non-compact Hamiltonian torus manifolds using index theory.

We study the problem of existence of geometric structures on compact complex surfaces that are related to split quaternions. These structures, called para-hypercomplex, para-hyperhermitian and para-hyperkähler are analogs of the hypercomplex, hyperhermitian and hyperkähler structures in the definite case. We show that …

Study on simplicity of Lie skew braces, proving new results for compact cases.

Study estimates area of non-compact surfaces in 3-manifolds, proving rigidity under certain conditions.

Proves almost flat spin^c manifolds bound compact manifolds.

Proves non-existence of certain metrics on specific manifolds.

We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show that, if the principal symbol class of such an elliptic operator on the boundary of …

Compact learning results across various loss functions.

Classifies Weyl structures on compact conformal manifolds with special holonomy.

Computes mapping class group orbits in surface framings.

Examining when Wu-Yau inequalities reach their maximum values.

New local method solves Yamabe problems on compact and non-compact manifolds.

The paper studies limits of sub-Riemannian Heisenberg manifolds and proves convergence under certain conditions.

The problem of minimal distortion bending of smooth compact embedded connected Riemannian $n$-manifolds $M$ and $N$ without boundary is made precise by defining a deformation energy functional $Φ$ on the set of diffeomorphisms $\diff(M,N)$. We derive the Euler-Lagrange equation for $Φ$ and determine smooth minimizers o…

Study existence of conformal metrics with specific curvature properties on compact manifolds.

Characterizes canonical elements in compact Lie algebras.

Characterizes kernels for forecasting and distinguishes between distributions.

A relatively simple algebraic framework is given, in which all the compact symmetric spaces can be described and handled without distinguishing cases. We also give some applications and further results.

Compact locally conformal Kähler manifolds with constant Chern holomorphic sectional curvature are necessarily Kähler.

Study on compact hypersurfaces in spheres with Ricci curvature bounds.

We prove the sharp estimate on the first nonzero eigenvalue of the p-laplacian on a compact Riemannian manifold with nonnegative Ricci curvature and possibly with convex boundary (in this case we assume Neumann b.c. on the p-laplacian). The proof is based on a gradient comparison theorem. We will also charachterize the…

In this paper we systematically describe relations between various structure sets which arise naturally for pairs of compact topological manifolds with boundary. Our consideration is based on a deep analogy between the case of a compact manifold with boundary and the case of a closed manifold pair. This approach also g…

Enhances Molino's description for foliated spaces, simplifying their study.