Isometrically embedded polydisks in infinite dimensional Teichmüller spacesThe Journal of Geometric Analysis - Tập 9 - Trang 51-71 - 1999
Clifford J. Earle, Zhong Li
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...... hiện toàn bộ
Almost Non-negative Scalar Curvature on Riemannian Manifolds Conformal to ToriThe Journal of Geometric Analysis - Tập 31 - Trang 11190-11213 - 2021
Brian Allen
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...... hiện toàn bộ
Small eigenvalues of geometrically finite manifoldsThe Journal of Geometric Analysis - Tập 14 Số 2 - Trang 281-290 - 2004
Hamenstädt, Ursula
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 domainsThe Journal of Geometric Analysis - Tập 1 - Trang 1-17 - 1991
Eric Bedford, Jiri Dadok
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 ...... hiện toàn bộ
Elements of functional calculus andL 2 regularity for some classes of fourier integral operatorsThe Journal of Geometric Analysis - Tập 16 - Trang 319-351 - 2006
Norberto Laghi
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...... hiện toàn bộ
Rigidity of Area-Minimizing Free Boundary Surfaces in Mean Convex Three-ManifoldsThe Journal of Geometric Analysis - Tập 25 - Trang 1001-1017 - 2013
Lucas C. Ambrozio
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...... hiện toàn bộ
Regularity Scales and Convergence of the Calabi FlowThe Journal of Geometric Analysis - Tập 28 - Trang 2050-2101 - 2017
Haozhao Li, Bing Wang, Kai Zheng
We define regularity scales to study the behavior of the Calabi flow. Based on estimates of the regularity scales, we obtain convergence theorems of the Calabi flow on extremal Kähler surfaces, under the assumption of global existence of the Calabi flow solutions. Our results partially confirm Donaldson’s conjectural picture for the Calabi flow in complex dimension 2. Similar results hold in high ...... hiện toàn bộ
On Pluripotential Theory Associated to Quaternionic m-Subharmonic FunctionsThe Journal of Geometric Analysis - Tập 33 - Trang 1-39 - 2023
Shengqiu Liu, Wei Wang
Many aspects of pluripotential theory are generalized to quaternionic m-subharmonic functions. We introduce quaternionic version of notions of the m-Hessian operator, m-subharmonic functions, m-Hessian measure, m-capacity, the relative m-extremal function, and the m-Lelong number, and show various propositions for them, based on
...... hiện toàn bộ