arXiv research

Extends ASD connection existence to 4-manifolds with cylindrical ends.

Study proves existence and uniqueness of Yang-Mills flow on cylindrical 4-manifolds.

We study the Yamabe invariants of cylindrical manifolds and compact orbifolds with a finite number of singularities, by means of conformal geometry and the Atiyah-Patodi-Singer $L^2$-index theory. For an $n$-orbifold $M$ with singularities $Σ_Γ = \{(\check{p}_1, Γ_1), ..., (\check{p}_s, Γ_s)\}$ (where each group $Γ_j<O…

We review the SO(3) instanton gauge theory of Fintushel and Stern and recast it in the context of 4-manifolds with cylindrical ends. Appli- cations to the Z/2-homology cobordism group of Z/2-homology 3-spheres are given.

Asymptotically cylindrical Ricci-flat manifolds play a key role in constructing Topological Quantum Field Theories. It is particularly important to understand their behavior at the cylindrical ends and the natural restrictions on the geometry. In this paper we show that an orientable, connected, asymptotically cylindri…

Finite number of eigenvalues found in cylindrical surface.

In this paper we announce a gluing theorem for conformal structures with anti-self-dual (ASD) Weyl tensor that applies in geometrical situations that are more general than those considered by previous authors. By adapting a method proposed by Floer, sufficient conditions are given for the existence of ASD conformal str…

Formulae prove equivalence of two invariants on specific 4-manifolds.

Study adiabatic limits of Calderon projector on manifolds with cylindrical ends.

We construct solutions of the vacuum vector constraint equations on manifolds with cylindrical ends.

Study well-posedness of generalized Stokes operator on cylindrical domains.

Study shows generic surfaces avoid complex flow patterns.

Let $X_0$ denote a compact, simply-connected smooth $4$-manifold with boundary the Poincaré homology $3$-sphere $Σ(2,3,5)$ and with even negative definite intersection form $Q_{X_0}=E_8$. We show that free $\mathbb{Z}/p$ actions on $Σ(2,3,5)$ do not extend to smooth actions on $X_0$ with isolated fixed points for any p…

Rotational symmetry proven for special self-expanders near cylinders.

Proves conjecture about special Lagrangians in G2-manifolds.

Paper proves uniqueness of special Lagrangian pair in Calabi-Yau 3-fold.

The paper constructs solutions to Kapustin-Witten equations with Nahm poles over manifolds with boundaries.

Defines new Roe algebras for cylindrical spaces, solving metric curvature problems.

We extend the study of the vacuum Einstein constraint equations on manifolds with ends of cylindrical type initiated by Chruściel and Mazzeo by finding a class of solutions to the fully coupled system on such manifolds. We show that given a Yamabe positive metric g, which is conformally asymptotically cylindrical on ea…

Ricci flow from spaces with cylindrical ends and unbounded curvature.

Researchers prove charged Penrose inequality and positive mass theorem for specific manifold types.

The study proves uniqueness of certain types of solitons.

We extend the Atiyah, Patodi, and Singer index theorem for first order differential operators from the context of manifolds with cylindrical ends to manifolds with periodic ends. This theorem provides a natural complement to Taubes' Fredholm theory for general end-periodic operators. Our index theorem is expressed in t…

We study a particular class of open manifolds. In the category of Riemannian manifolds these are complete manifolds with cylindrical ends. We give a natural setting for the conformal geometry on such manifolds including an appropriate notion of the cylindrical Yamabe constant/invariant. This leads to a corresponding ve…

This thesis studies moduli spaces of singular connections on 3-manifolds and manifolds with cylindrical ends. A Chern-Simons functional is defined for singular connections on 3-manifolds which are singular along a knot. The critical points of that Chern-Simons functional are flat singular connections. The Hodge-de Rham…

New calculus for pseudodifferential operators on manifolds with cylindrical ends.

We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G_2 structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that the holonomy of the induced metric of an exponentially asymptotically…

The study analyzes spectral asymmetry and index theory on manifolds with generalized hyperbolic cusps.

Study steady gradient Ricci solitons with cylindrical tangent flows at infinity.

Study shows nonnegative curvature metrics have complex homotopy structure.

Study shows inequalities for 4-manifolds with periodic ends and constructs new non-SC manifolds.

New insights into manifold properties using Seiberg-Witten and $L^2$ harmonic theories.

Paper proves finite Morse index for certain self-shrinkers.

Symplectic stability holds for noncompact manifolds with specific end conditions.

The paper constructs harmonic 1-forms on 3-manifolds with cylindrical necks.

Extends Taubes's theorem to non-compact manifolds with harmonic forms.

Proves existence of initial data with specific curvature properties for Einstein equations.

Surveying interactions between foliations and contact structures in 3D.

Compact theorem for $SO(3)$ anti-self-dual equations on cylindrical manifolds.

Given two unitary involutions $σ_{1}$ and $σ_{2}$ satisfying $G σ_{i} = - σ_{i} G$ on $ker B$ on a compact manifold with cylindrical end, M. Lesch, K. Wojciechowski ([LW]) and W. Müller ([M]) established the formula describing the difference of two eta-invariants with the APS boundary conditions associated with $σ_{1}$…

Let $M$ be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to $[0,\infty) \times X$ for some compact connected Ricci-flat manifold $X$. We begin by proving general structure theorems for $M$; in particular we show that there is no loss of generality in assumi…

In this paper we present a way of computing a lower bound for genus of any smooth representative of a homology class of positive self-intersection in a smooth four-manifold $X$ with second positive Betti number $b_2^+(X)=1$. We study the solutions of the Seiberg-Witten equations on the cylindrical end manifold which is…

Analyzes Seiberg-Witten theory on 4-manifolds with periodic ends, proving invariants and compactness.

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity…

Researchers found multiple ways to end-sum 4-manifolds, contradicting a previous conjecture.

We establish the basics of the analysis of operators on coverings of manifolds with cylindrical ends with a group of deck transformations $Γ$. We prove the $Γ$-analogue of the Atiyah-Patodi-Singer formula for Dirac operators on such coverings.

We use Furuta's result, usually referred to as ``10/8-conjecture'', to show that for any compact 3-manifold $M$ the open manifold $M\times\r$ has infinitely many different smooth structures. Another consequence of Furuta's result is existence of infinitely many smooth structures on open topological 4-manifolds with a t…

We prove that all Lagrangian spheres in S^2 x S^2 are Hamiltonian isotopic. The proof uses various properties of holomorphic curves in symplectic manifolds with cylindrical ends which were recently developed in connection with the Symplectic Field Theory.