A Characterization of Codimension One Collapse Under Bounded Curvature and Diameter [0.03%]
曲率和直径有界的 codimension one 情形的塌陷性质刻画
Saskia Roos
Saskia Roos
Let M ( n , D ) be the space of closed n-dimensional Riemannian manifolds (M, g) with diam ( M ) ≤ D and | sec M | ≤ 1 . In this paper we consider sequences ( M i , g i ) in M ( n , D ) converging in the Gromov-Hausdorff ...
Ivan Cheltsov
Ivan Cheltsov
We prove that 2 d , 2 d - 3 ( d - 1 ) 2 , 2 d - 1 d ( d - 1 ) , 2 d - 5 d 2 - 3 d + 1 and 2 d - 3 d ( d - 2 ) are the smallest log canonical thresholds of reduced plane curves of degree d ⩾ 3 , and we describe reduced plane...
Intrinsic Flat and Gromov-Hausdorff Convergence of Manifolds with Ricci Curvature Bounded Below [0.03%]
具有下界Ricci曲率的流形的内在平坦和Gromov-Hausdorff收敛性
Rostislav Matveev,Jacobus W Portegies
Rostislav Matveev
We show that for a noncollapsing sequence of closed, connected, oriented Riemannian manifolds with Ricci curvature bounded below and diameter bounded above, Gromov-Hausdorff convergence agrees with intrinsic flat convergence. In particular,...
Gauge Theory on Projective Surfaces and Anti-self-dual Einstein Metrics in Dimension Four [0.03%]
投影曲面上的规范理论和四维中的反自对偶爱因斯坦度量
Maciej Dunajski,Thomas Mettler
Maciej Dunajski
Given a projective structure on a surface N , we show how to canonically construct a neutral signature Einstein metric with non-zero scalar curvature as well as a symplectic form on the total space M of a certain rank 2 affine bundle M U...
Peter Pflug,Włodzimierz Zwonek
Peter Pflug
We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a descripti...
Global Weak Rigidity of the Gauss-Codazzi-Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower Regularity [0.03%]
带较低正则性的Gauss-Codazzi-Ricci方程的全局弱 rigidity及黎曼流形的等距嵌入
Gui-Qiang G Chen,Siran Li
Gui-Qiang G Chen
We are concerned with the global weak rigidity of the Gauss-Codazzi-Ricci (GCR) equations on Riemannian manifolds and the corresponding isometric immersions of Riemannian manifolds into the Euclidean spaces. We develop a unified intrinsic a...
Julius Ross,Michael Singer
Julius Ross
We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor Y. Assuming the data in question is invariant under an S 1 ...
The Trace Theorem, the Luzin N- and Morse-Sard Properties for the Sharp Case of Sobolev-Lorentz Mappings [0.03%]
Sobolev-Lorentz映射的迹定理、Luzin N-和Morse-Sard性质（Sharp情形）
Mikhail V Korobkov,Jan Kristensen
Mikhail V Korobkov
We prove Luzin N- and Morse-Sard properties for mappings v : R n → R d of the Sobolev-Lorentz class W p , 1 k , p = n k (this is the sharp case that guaranties the continuity of mappings). Our main tool is a new trace theorem fo...
Morrey Spaces on Domains: Different Approaches and Growth Envelopes [0.03%]
Morrey域上的空间：不同的方法和增长-envelope
Dorothee D Haroske,Cornelia Schneider,Leszek Skrzypczak
Dorothee D Haroske
We deal with Morrey spaces on bounded domains Ω obtained by different approaches. In particular, we consider three settings M u , p ( Ω ) , M u , p ( Ω ) and M u , p ( Ω ) , where 0
Weak and Strong Type [Formula: see text] - [Formula: see text] Estimates for Sparsely Dominated Operators [0.03%]
稀疏支配算子的弱型和强型[Formula: see text]-[Formula: see text]估计式
Dorothee Frey,Zoe Nieraeth
Dorothee Frey
We consider operators T satisfying a sparse domination property | ⟨ T f , g ⟩ | ≤ c ∑ Q ∈ S ⟨ f ⟩ p 0 , Q ⟨ g ⟩ q 0 ' , Q | Q | with averaging exponents 1 ≤ p 0