The Journal of Geometric Analysis
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Isometrically embedded polydisks in infinite dimensional Teichmüller spaces
The Journal of Geometric Analysis - Tập 9 - Trang 51-71 - 1999
We define isometric holomorphic embeddings of the infinite dimensional polydisk D∞ in any infinite dimensional Teichmüller space. These embeddings provide simple new proofs that the Teichmüller metric on any infinite dimensional Teichmüller space is non-differentiable and has arbitrarily short simple closed geodesics. They also lead to a complete characterization of the points in Teichmüller space......
Almost Non-negative Scalar Curvature on Riemannian Manifolds Conformal to Tori
The Journal of Geometric Analysis - Tập 31 - Trang 11190-11213 - 2021
In this article we reduce the geometric stability conjecture for the scalar torus rigidity theorem to the conformal case via the Yamabe problem. Then we are able to prove the case where a sequence of Riemannian manifolds is conformal to a uniformly controlled sequence of flat tori and satisfies the geometric stability conjecture. We are also able to handle the case where a sequence of Riemannian m......
Small eigenvalues of geometrically finite manifolds
The Journal of Geometric Analysis - Tập 14 Số 2 - Trang 281-290 - 2004
Let M be a complete geometrically finite manifold of bounded negative curvature, infinite volume, and dimension at least 3.We give both a lower bound for the bottom of the spectrum of M and an upper bound for the number of the small eigenvalues of M. These bounds only depend on the dimension, curvature bounds and the volume of the oneneighborhood of the convex core.
Generalized reinhardt domains
The Journal of Geometric Analysis - Tập 1 - Trang 1-17 - 1991
In this paper we investigate a class of Lie group actions on
$$\mathbb{C}^N $$
, the so-calledpolar actions, that naturally generalize the standard
$$\mathbb{T}^N $$
actions. For a domain invariant under such ......
Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups
The Journal of Geometric Analysis - Tập 13 Số 2 - Trang 301-328 - 2003
Elements of functional calculus andL 2 regularity for some classes of fourier integral operators
The Journal of Geometric Analysis - Tập 16 - Trang 319-351 - 2006
We employ the method of slices to develop a rudimentary calculus describing the nature of operators T*T (respectively, TT*), where T are Fourier integral operators with one-sided right (respectively, left) singularities; this idea has its roots in the work of Greenleaf and Seeger. Such a result allows us to reduce the L2 regularity problem for operators in n dimensions with one-sided singularities......
Some Remarks on Willmore Surfaces Embedded in $${\mathbb {R}}^3$$
The Journal of Geometric Analysis - Tập 26 - Trang 2411-2424 - 2015
Let
$$f:{\mathbb {C}}\rightarrow {\mathbb {R}}^3$$
be a complete Willmore immersion with
$$\int _{\Sigma }|A_f|^2<+\infty $$
......
Rigidity of Area-Minimizing Free Boundary Surfaces in Mean Convex Three-Manifolds
The Journal of Geometric Analysis - Tập 25 - Trang 1001-1017 - 2013
We prove a local splitting theorem for three-manifolds with mean convex boundary and scalar curvature bounded from below that contain certain locally area-minimizing free boundary surfaces. Our methods are based on those of Micallef and Moraru (Splitting of 3-manifolds and rigidity of area-minimizing surfaces,
arXiv:1107.5346
, 2011). We use th......
Two-Dimensional Martingale Transforms and Their Applications in Summability of Walsh–Fourier Series
The Journal of Geometric Analysis - Tập 33 - Trang 1-19 - 2023
In the paper, we are going to prove that the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series is bounded from
$$L\log L\left( (0,1]\times (0,1]\right) $$
to
$$L_{1,\infty }((0,1]\times ......
Local Tb Theorems and Hardy Inequalities
The Journal of Geometric Analysis - Tập 23 Số 1 - Trang 303-374 - 2013
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