Rafael B Andrist,Gaofeng Huang
Rafael B Andrist
We show that the direct product of two Stein manifolds with the Hamiltonian density property enjoys the Hamiltonian density property as well. We investigate the relation between the Hamiltonian density property and the symplectic density pr...
Pólya-Szegő Inequalities on Submanifolds with Small Total Mean Curvature [0.03%]
小总平均曲率子流形上的Pólya-Szegő不等式
Pietro Aldrigo,Zoltán M Balogh
Pietro Aldrigo
We establish Pólya-Szegő-type inequalities (PSIs) for Sobolev-functions defined on a regular n-dimensional submanifold Σ (possibly with boundary) of a ( n + m ) -dimensional Euclidean space, under explicit upper bounds of the total ...
Ray Transform of Symmetric Tensor Fields on Riemannian Manifolds with Conjugate Points [0.03%]
具有一对共轭点的黎曼流形上对称张量场的射线变换
Sean Holman,Venkateswaran P Krishnan
Sean Holman
In this article, we study the microlocal properties of the geodesic ray transform of symmetric m-tensor fields on 2-dimensional Riemannian manifolds with boundary allowing the possibility of conjugate points. As is known from an earlier wor...
Daniel Tsodikovich
Daniel Tsodikovich
We show a local rigidity result for the integrability of symplectic billiards. We prove that any domain which is close to an ellipse, and for which the symplectic billiard map is rationally integrable must be an ellipse as well. This is in ...
Symbolic Calculus for a Class of Pseudodifferential Operators with Applications to Compactness [0.03%]
一类伪微分算子的符号演算及其在紧性的应用
Árpád Bényi,Tadahiro Oh,Rodolfo H Torres
Árpád Bényi
We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to L 2 -compactness via a compact version of the T(1) theorem. ...
Amlan Banaji,Alex Rutar,Sascha Troscheit
Amlan Banaji
The ϕ -Assouad dimensions are a family of dimensions which interpolate between the upper box and Assouad dimensions. They are a generalization of the well-studied Assouad spectrum with a more general form of scale sensitivity that is o...
A Unifying Framework for Complex-Valued Eigenfunctions via The Cartan Embedding [0.03%]
基于Cartan嵌入的复特征值函数研究统一框架
Sigmundur Gudmundsson,Adam Lindström
Sigmundur Gudmundsson
In this work we find a unifying scheme for the known explicit complex-valued eigenfunctions on the classical compact Riemannian symmetric spaces. For this we employ the well-known Cartan embedding for those spaces. This also leads to the co...
Joonas Ilmavirta,Antti Kykkänen,Matti Lassas et al.
Joonas Ilmavirta et al.
We prove that the reconstruction of a certain type of length spaces from their travel time data on a closed subset is Lipschitz stable. The travel time data is the set of distance functions from the entire space, measured on the chosen clos...
Hunter Stufflebeam,Paul Sweeney Jr
Hunter Stufflebeam
In 2018, Marques and Neves proposed a volume preserving intrinsic flat stability conjecture concerning their width rigidity theorem for the unit round 3-sphere. In this work, we establish the validity of this conjecture under the additional...
Geometric Bounds for Low Steklov Eigenvalues of Finite Volume Hyperbolic Surfaces [0.03%]
双曲曲面上低Steklov特征值的几何界
Asma Hassannezhad,Antoine Métras,Hélène Perrin
Asma Hassannezhad
We obtain geometric lower bounds for the low Steklov eigenvalues of finite-volume hyperbolic surfaces with geodesic boundary. The bounds we obtain depend on the length of a shortest multi-geodesic disconnecting the surfaces into connected c...