arXiv research

Extends soliton theory to non-compact cases.

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

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

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

Study finds solutions for complex problems on non-compact manifolds.

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

Proves non-existence of certain metrics on specific manifolds.

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

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

In this paper, we give a delay estimate of scalar curvature for a complete non-compact expanding (or steady) gradient Ricci soliton with nonnegative Ricci curvature. As an application, we prove that any complete non-compact expanding (or steady) gradient Kähler-Ricci solitons with positively pinched Ricci curvature sho…

We formulate a conjecture that arithmetic locally symmetric manifolds have simple homotopy type, and prove it for the non-compact case. More precisely, we show that, for any symmetric space S of non-compact type without Euclidean de Rham factors, there are constants a=a(S) and d=d(S) such that any non-compact arithmeti…

Study eta invariant on non-compact manifolds with positive scalar curvature.

In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open existence problem in the real and quaternionic cases.

Upper bounds for Laplace eigenvalues on non-compact manifolds.

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

Study of eta invariant for non-compact manifolds via Dirac-type operators.

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

Study of Sasakian immersions in Heisenberg group and $\mathbb{B}^N imes \mathbb{R}$, focusing on $η$-Einstein case.

The paper extends rigidity results to non-compact domains and infinite energy maps.

Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.

Study harmonic metrics on Higgs bundles on non-compact Riemann surfaces.

Study of elliptic boundary value problems on non-compact manifolds.

The study finds surface subgroups in cocompact lattices of $H^{2n}$ for $n\geq2$.

Study preserves tubeness of tubes in certain symmetric spaces.

Harmonic metrics are established for SO0(n,n)-Higgs bundles on non-compact hyperbolic surfaces.

Extends Atiyah-Singer Dirac operator study to non-compact spacetimes.

Variant of previous work on smooth algebraic functions with compact and non-compact preimages.

The study counts ends on shrinkers using geometric covering methods.

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…

New example shows non-compact manifolds can lack $L^p$-Calderón-Zygmund inequalities.

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 …

Develops an equivariant index for non-compact group actions.

We prove existence of isoperimetric regions for every volume in non-compact Riemannian $n$-manifolds $(M,g)$, $n\geq 2$, having Ricci curvature $Ric_g\geq (n-1) k_0 g$ and being locally asymptotic to the simply connected space form of constant sectional curvature $k_0$; moreover in case $k_0=0$ we show that the isoperi…

Classifies $π_1$-injective maps between non-compact surfaces.

New theorems on non-compact manifolds using dynamical methods.

Paper proves a theorem for Higgs bundles on certain non-compact manifolds.

The study extends conserved quantities theory to non-compact boundary initial data sets.

In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform estimates via Gromov's covering lemma, we provide a Coulhon, Saloff-Coste and Varopo…

Study the APS index theorem for even-dimensional manifolds with non-compact boundaries.

Assigns compact set distance-like functions to non-compact geodesic spaces.

Study Szegő kernel on non-compact CR manifolds with specific conditions.

Essential self-adjointness proven for powers of first-order differential operators on non-compact manifolds with low-regularity metrics.

We prove a Lichnerowicz type vanishing theorem for non-compact spin manifolds admiting proper cocompact actions. This extends a previous result of Ziran Liu who proves it for the case where the acting group is unimodular.

The paper extends Yamabe flow results to non-compact manifolds with bounded geometry.

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Dirac-type equations with these boundary conditio…

New proof shows perturbed non-compact Einstein spaces attract to unique global solution.

Sharp lower bound for $p$-Laplacian eigenvalue on non-compact manifolds.

Strong rigidity proven for non-compact surfaces.