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Injectivity and Stability for a Generic Class of Generalized Radon Transforms. 一类广义Radon变换的注入性和稳定性。
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2017-01-01 Epub Date: 2016-06-30 DOI: 10.1007/s12220-016-9729-4
Andrew Homan, Hanming Zhou

Let (M, g) be an analytic, compact, Riemannian manifold with boundary, of dimension n ≥ 2 . We study a class of generalized Radon transforms, integrating over a family of hypersurfaces embedded in M, satisfying the Bolker condition (in: Quinto, Proceedings of conference "Seventy-five Years of Radon Transforms", Hong Kong, 1994). Using analytic microlocal analysis, we prove a microlocal regularity theorem for generalized Radon transforms on analytic manifolds defined on an analytic family of hypersurfaces. We then show injectivity and stability for an open, dense subset of smooth generalized Radon transforms satisfying the Bolker condition, including the analytic ones.

设(M, g)是一个解析的、紧的、边界为n≥2维的黎曼流形。我们研究了一类广义Radon变换，在M中嵌入的超曲面族上积分，满足Bolker条件(见:Quinto，会议论文集“Radon变换的75年”，香港，1994)。利用解析微局部分析，证明了定义在解析超曲面族上的解析流形上广义Radon变换的一个微局部正则性定理。然后，我们证明了满足Bolker条件的光滑广义Radon变换的开放稠密子集(包括解析子集)的注入性和稳定性。
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引用次数: 20
The Variations of Yang–Mills Lagrangian 杨-米尔斯拉格朗日量的变化
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2015-06-15 DOI: 10.1007/978-3-030-34953-0_15
T. Rivière
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引用次数: 8
On Brunn–Minkowski-Type Inequalities for Polar Bodies 关于极体的brunn - minkowski型不等式
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2014-09-18 DOI: 10.1007/s12220-014-9541-y
M. A. Hernández Cifre, J. Yepes Nicolás
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引用次数: 1
A Disc Formula for Plurisubharmonic Subextensions in Manifolds 流形中多次调和子扩展的圆盘公式
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2014-03-21 DOI: 10.1007/s12220-014-9474-5
B. Drinovec Drnovšek
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引用次数: 1
The Paley–Wiener Theorem and Limits of Symmetric Spaces 对称空间的Paley-Wiener定理与极限
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2013-11-06 DOI: 10.1007/s12220-013-9467-9
G. Ólafsson, J. Wolf
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引用次数: 12
Reduction of Five-Dimensional Uniformly Levi Degenerate CR Structures to Absolute Parallelisms 五维均匀Levi简并CR结构的绝对平行化
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2013-04-10 DOI: 10.1007/s12220-013-9419-4
A. Isaev, D. Zaitsev
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引用次数: 47
On the Best Pinching Constant of Conformal Metrics on $mathbb {S}^{2}$ with One and Two Conical Singularities 关于$mathbb {S}^{2}$上具有一个和两个圆锥奇点的共形度量的最佳捏紧常数
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2013-04-01 DOI: 10.1007/S12220-011-9266-0
D. Bartolucci
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引用次数: 25
Logarithmic Lp Bounds for Maximal Directional Singular Integrals in the Plane 平面上最大方向奇异积分的对数Lp界
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2012-10-03 DOI: 10.1007/s12220-012-9340-2
C. Demeter, Francesco Di Plinio
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引用次数: 28
Solutions of Semilinear Elliptic Equations in Tubes 管内半线性椭圆方程的解
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2012-10-03 DOI: 10.1007/s12220-012-9342-0
F. Pacard, F. Pacella, B. Sciunzi
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引用次数: 11
Linearity and Second Fundamental Forms for Proper Holomorphic Maps from $mathbb{B}^{n+1}$ to $mathbb{B}^{4n-3}$ $mathbb{B}^{n+1}$到$mathbb{B}^{4n-3}$的固有全纯映射的线性和第二基本形式
IF 1.1 2区 数学 Q1 MATHEMATICS
Journal of Geometric Analysis
Pub Date : 2012-10-01 DOI: 10.1007/S12220-011-9225-9
Xiaoliang Cheng, S. Ji
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引用次数: 2
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