Xianzhe Dai, Guofang Wei
We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with asymptotic geometry at infinity. The asymptotic geometry at infinity is either a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a cone with a compact fiber (the fibered boundary). Many noncompact Einstein manifolds come with such a geometry at infinity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this short paper, we prove a Hitchin-Thorpe type inequality for closed 4-manifolds with non-positive Yamabe invariant, and admitting long time solutions of the normalized Ricci flow equation with bounded scalar curvature.
In this article, we investigate the geometry of $4$-dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a $4$-dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.
In this article, stimulated by Fernandez-Lopez and Garcia-Rio, we shall give an upper diameter bound for compact Ricci solitons in terms of the range of the scalar curvature. As an application, we shall provide some sufficient conditions for four-dimensional compact Ricci solitons to satisfy the Hitchin-Thorpe inequality.
We prove a Hitchin-Thorpe inequality for noncompact 4-manifolds with foliated geometry at infinity by extending on previous work by Dai and Wei. After introducing the objects at hand, we recall some preliminary results regarding the $G$-signature formula and the rho invariant, which are used to obtain expressions for the signature and Euler characteristic in our geometric context. We then derive our main result, and present examples.
We prove that a compact, connected, and oriented 4-dimensional gradient $m$-quasi-Einstein manifold with $m\in [1, \infty]$ which is additionally a spin manifold must satisfy the Hitchin-Thorpe Inequality. We show further that the homeomorphism-type of the universal cover of such a manifold is either $S^4$ or a connected sum of some number of $S^2\times S^2$ when the potential function is nontrivial.
Diameter estimates and Hitchin-Thorpe inequality for four-dimensional compact Quasi-Einstein manifolds
研究四维紧致m-拟爱因斯坦流形的直径估计，基于势函数的振荡性推导几何界，提出确保满足希奇-托尔佩不等式的直径条件，扩展了光滑度量测度空间的直径估计结果。
Hodge Splittings and Einstein 4-manifolds
研究四维流形上满足曲率张量保持由h确定的Hodge分裂的Riemannian度量对，扩展了四维爱因斯坦条件，并通过变分方法分析了混合爱因斯坦-希尔伯特函数的临界点。
An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces are proved.
In this paper, we study the existence of Poisson metrics on flat vector bundles over noncompact Riemannian manifolds and discuss related consequence, specially on the applications in Higgs bundles, towards generalizing Corlette-Donaldson-Hitchin-Simpson's nonabelian Hodge correspondence to noncompact Kähler manifolds setting.
We develop a notion of Einstein manifolds with skew torsion on compact, orientable Riemannian manifolds of dimension four. We prove an analogue of the Hitchin-Thorpe inequality and study the case of equality. We use the link with self-duality to study the moduli space of 1-instantons on the 4-sphere for a family of metrics defined by Bonneau.
Inequalities for 4-Manifolds with Ends using Fibered boundary metric and Seiberg-Witten Equations
本文利用Hitchin-Thorpe不等式与Seiberg-Witten方程，为具有纤维边界或尖点度量的非紧四维流形建立新不等式，并证明边界纤维为单点时的情形。
In this paper, we investigate the geometry of asymptotically flat manifolds with controlled holonomy. We show that any end of such manifold admits a torus fibration over an ALE end. In addition, we prove a Hitchin-Thorpe inequality for oriented Ricci-flat $4$-manifolds with curvature decay and controlled holonomy. As an application, we show that any complete asymptotically flat Ricci-flat metric on a $4$-manifold which is homeomorphic to $\mathbb R^4$ must be isometric to the Euclidean or the Taub-NUT metric, provided that the tangent cone at infinity is not $\mathbb R \times \mathbb R_+$.
It is shown that there are infinitely many compact orientable smooth 4-manifolds which do not admit Einstein metrics, but nevertheless satisfy the strict Hitchin-Thorpe inequality 2 chi > 3 |tau|. The examples in question arise as non-minimal complex algebraic surfaces of general type, and the method of proof stems from Seiberg-Witten theory.
We show that there exist smooth, simply connected, four-dimensional spin manifolds which do not admit Einstein metrics, but nonetheless satisfy the strict Hitchin-Thorpe inequality. Our construction makes use of the Bauer/Furuta cohomotopy refinement of the Seiberg-Witten invariant, in conjunction with curvature estimates previously proved by the second author. These methods also easily allow one to construct examples of topological 4-manifolds which admit an Einstein metric for one smooth structure, but which have infinitely many other smooth structures for which no Einstein metric can exist.
We introduce the notion of a special monopole class on a four-manifold. This is used to prove restrictions on the smooth structures of Einstein manifolds. As an application we prove that there are Einstein four-manifolds which are simply connected, spin, and satisfy the strict Hitchin--Thorpe inequality, and which are homeomorphic to manifolds without Einstein metrics. In the Appendix, written with J. Wehrheim, we use special monopole classes to discuss the classification of Ricci-flat four-manifolds.
We construct infinitely many examples of finite volume 4-manifolds with $T^3$ ends that do not admit any cusped asymptotically hyperbolic Einstein metrics yet satisfy a strict logarithmic version of the Hitchin-Thorpe inequality due to Dai-Wei. This is done by using estimates from Seiberg-Witten theory due to LeBrun as well as a method for constructing solutions to the Seiberg-Witten equations on noncompact manifolds due to Biquard. We also use constructions coming from the $Pin^-(2)$ monopole equations to obtain a larger class of manifolds where these techniques apply.
We show that the minimal volume entropy of closed manifolds remains unaffected when nonessential manifolds are added in a connected sum. We combine this result with the stable cohomotopy invariant of Bauer-Furuta in order to present an infinite family of four-manifolds with the following properties: 1) They have positive minimal volume entropy. 2) They satisfy a strict version of the Gromov-Hitchin-Thorpe inequality, with a minimal volume entropy term. 3) They nevertheless admit infinitely many distinct smooth structures for which no compatible Einstein metric exists.
We survey the definitions and some important properties of several asymptotic invariants of smooth manifolds, and discuss some open questions related to them. We prove that the (non-)vanishing of the minimal volume is a differentiable property, which is not invariant under homeomorphisms. We also formulate an obstruction to the existence of Einstein metrics on four-manifolds involving the volume entropy. This generalizes both the Gromov--Hitchin--Thorpe inequality and Sambusetti's obstruction.
Fractal closures of geodesic planes in Hitchin manifolds
该研究通过构造 Hitchin 流形中的漂浮测地平面，证明了其闭包为分形，揭示了高秩无限体积情况下非紧类型局部对称空间的拓扑刚性反例。
Hermitian-Einstein equations on noncompact manifolds
本文研究非紧流形上Hermitian-Einstein方程的可解性与唯一性，证明稳定性并建立Kobayashi-Hitchin对应，推广至更一般情形。
Complete noncompact G2-manifolds with ALC asymptotics
研究了具有ALC渐近性的完整非紧7维G2holonomy度量的存在性、唯一性和结构结果，提出G2流形的Atiyah-Hitchin度量类比及ALC度量的良好模空间理论。
Compact toric Einstein four-manifolds
本文发展了紧致单连通环面爱因斯坦四流形的系统理论，通过局部粘合与虚拟计数构造任意大$b_2$的正爱因斯坦度量，并给出代数特殊度量的拓扑刻画、唯一性及微分同胚分类。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。