Infinitely many singular interactions on noncompact manifolds

We show that the ground state energy is bounded from below when there are infinitely many attractive delta function potentials placed in arbitrary locations, while all being separated at least by a minimum distance, on two dimensional non-compact manifold. To facilitate the reading of the paper, we first present the arguments in the setting of Cartan–Hadamard manifolds and then subsequently discuss the general case. For this purpose, we employ the heat kernel techniques as well as some comparison theorems of Riemannian geometry, thus generalizing the arguments in the flat case following the approach presented in Albeverio et al. (2004).     

A new characterization of the Berger sphere in complex projective space

We give a complete classification of Lagrangian immersions of homogeneous 3-manifolds (the Berger spheres, the Heisenberg group ${\text{Nil}}_3$, the universal covering of the Lie group $\text{PSL}(2,\mathbb{R})$ and the Lie group ${\text{Sol}}_3$) in 3-dimensional complex space forms. As a corollary, we get a new characterization of the Berger sphere in complex projective space.     

Nonlocal Interaction Equations in Environments with Heterogeneities and Boundaries

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets ? of ? ^d endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqueness and stability of solutions. We study the equations in the setting of gradient flows in the space of probability measures on ? endowed with Riemannian 2-Wasserstein metric.     

右半结肠癌完全结肠系膜切除术清扫肠系膜根部淋巴结效果观察

目的 探讨右半结肠癌行完全结肠系膜切除术（CME）清扫肠系膜根部淋巴结的临床疗效。方法 以2010年12月 至2012 年12 月行CME 的57 例右半结肠癌患者作为观察组,同期接受传统结肠癌根治术的99 例右半结肠癌患者作为对照组,对两组患者的淋巴结清扫数量、平均出血量、手术时间、住院时间、术后排气、排便时间、手术并发症、2年局部复发率及生存率等情况进行比较,初步评价CME 清扫肠系膜根部淋巴结的临床效果。结果 CME 组与对照组总淋巴结清扫数量分别为（22.6±2.8）、（14.6±2.7）枚,CME 组淋巴结清扫数量明显多于对照组（P＜0.05）;CME 组平均出血量为（167.4±20.8）ml,对照组为（205.4±19.3）ml,CME 组出血量少于对照组（P＜0.05）;两组的手术时间、住院时间、术后排气、排便时间比较差异均无统计学意义（均P＞0.05）;CME 组手术并发症发生率与对照组比较差异无统计学意义（P ＞0.05）;Ⅲ期患者CME 组2 年局部复发率38.2％、生存率88.2％,对照组分别为64.8％和68.5％,两组差异有统计学意义（均P＜0.05）。结论 右半结肠癌患者采用CME 清扫肠系膜根部 淋巴结是安全和有效的。     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

局部对称的黎曼流形中的极小子流形

主要研究了局部对称的黎曼流形中的定向紧致无边极小子流形的内蕴刚性问题,利用一个矩阵不等式,得到了这类子流形的一个刚性定理．所得结果部分改进了已有的一个结论．     

Quaternionic structures

Any oriented 4-dimensional real vector bundle is naturally a line bundle over a bundle of quaternion algebras. In this paper we give an account of modules over bundles of quaternion algebras, discussing Morita equivalence, characteristic classes and K-theory. The results have been used to describe obstructions for the existence of almost quaternionic structures on 8-dimensional Spin^c manifolds in ?adek et al. (2008) [5] and may be of some interest, also, in quaternionic and algebraic geometry.     

Topology of complete intersections

Let X _n (d) and X _n (d') be two n-dimensional complete intersections with the same total degree d. In this paper we prove that, if n is even and d has no prime factors less than , then X _n (d) and X _n (d') are homotopy equivalent if and only if they have the same Euler characteristics and signatures. This confirms a conjecture of Libgober and Wood [16]. Furthermore, we prove that, if d has no prime factors less than , then X _n (d) and X _n (d') are homeomorphic if and only if their Pontryagin classes and Euler characteristics agree. Received: September 6, 1996