The Journal of Geometric Analysis
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On the solutions to certain laplace inequalities with applications to geometry of submanifolds
The Journal of Geometric Analysis - Tập 2 - Trang 195-211 - 1992
LetM be a complete Riemannian manifold with Ricci curvature bounded from below. We give an explicit estimate for the size of the negative sets of solutions to the differential inequality Δu ≥λu where Δ is the Laplacian and λ is a negative constant. This inequality arises naturally when we study the lengthH of the mean curvature of an isometric immersionf of M into another Riemannian manifoldN with...... hiện toàn bộ
Radon-Type Transforms for Holomorphic Functions in the Lie Ball
The Journal of Geometric Analysis - Tập 29 - Trang 2709-2737 - 2018
In this paper, we consider holomorphic functions on the m-dimensional Lie ball LB(0, 1) which admit a square integrable extension on the Lie sphere. We then define orthogonal projections of this set onto suitable subsets of functions defined in lower- dimensional spaces to obtain several Radon-type transforms. For all these transforms we provide the kernel and an integral representation, besides o...... hiện toàn bộ
On a Classification of 4-d Gradient Ricci Solitons with Harmonic Weyl Curvature
The Journal of Geometric Analysis - Tập 27 - Trang 986-1012 - 2016
We study a characterization of 4-dimensional (not necessarily complete) gradient Ricci solitons (M, g, f) which have harmonic Weyl curvature, i.e.,
$$\delta W=0$$
. Roughly speaking, we prove that the soliton metric g is locally isometric to one o...... hiện toàn bộ
Invariant currents and dynamical Lelong numbers
The Journal of Geometric Analysis - Tập 14 - Trang 199-213 - 2004
Let ƒ be a polynomial automorphism of ℂk of degree λ, whose rational extension to ℙk maps the hyperplane at infinity to a single point. Given any positive closed current S on ℙk of bidegree (1,1), we show that the sequence λ−n(ƒn)*S converges in the sense of currents on ℙk to a linear combination of the Green current T+ of ƒ and the current of integration along the hyperplane at infinity. We give ...... hiện toàn bộ
CMC Foliations of Closed Manifolds
The Journal of Geometric Analysis - Tập 26 - Trang 1647-1677 - 2015
We prove that every closed, smooth
$$n$$
-manifold
$$X$$
admits a Riemannian metric together ...... hiện toàn bộ
Lusin-Type Properties of Convex Functions and Convex Bodies
The Journal of Geometric Analysis - - 2021
Laplacian Flow of Closed G $$_2$$ -Structures Inducing Nilsolitons
The Journal of Geometric Analysis - Tập 26 - Trang 1808-1837 - 2015
We study the existence of left invariant closed
$$G_2$$
-structures defining a Ricci soliton metric on simply connected nonabelian nilpotent Lie groups. For each one of these
...... hiện toàn bộ
Finite jet determination of CR embeddings
The Journal of Geometric Analysis - Tập 14 - Trang 241-265 - 2004
We prove finite jet determination results for smooth CR embeddings, which are of constant degeneracy, using the method of complete systems. As an application, we obtain a reflection principle for mappings between a Levinondegenerate hypersurface in ℂ
N
and a Levinondegenerate hypersurface in ℂN+1.We also give an independent proof of the reflection principle for ma...... hiện toàn bộ
Hypersurfaces of Constant Curvature in Hyperbolic Space I
The Journal of Geometric Analysis - Tập 19 Số 4 - Trang 772-795 - 2009
Non-homogeneous Tb Theorem and Random Dyadic Cubes on Metric Measure Spaces
The Journal of Geometric Analysis - - 2011
We prove a Tb theorem on quasimetric spaces equipped with what we call an upper doubling measure. This is a property that encompasses both the doubling measures and those satisfying the upper power bound μ(B(x,r))≤Cr
d
. Our spaces are only assumed to satisfy the geometric doubling property: every ball of radius r can be covered by at most N balls...... hiện toàn bộ
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