The Journal of Geometric Analysis
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Soliton Solutions for Quasilinear Schrödinger Equations Involving Convolution and Critical Nonlinearities
The Journal of Geometric Analysis - Tập 32 - Trang 1-48 - 2021
In this paper, we establish the existence, multiplicity and concentration
behaviour of positive solutions for quasilinear Schrödinger equations with
Choquard term and critical nonlinearities: $$\begin{aligned} -\varepsilon
^{p}(\Delta _p u+u\Delta _p(u^2))+ V(x)|u|^{p-2}u = \varepsilon ^{\mu -N}\left(
|x|^{-\mu }*F(u)\right) f(u) + |u|^{2p^*-2}u, \end{aligned}$$ where
$$\varepsilon >0$$ is a param...
Global Well-Posedness to the Cauchy Problem of Two-Dimensional Nonhomogeneous Heat Conducting Navier-Stokes Equations
The Journal of Geometric Analysis - Tập 32 - Trang 1-22 - 2022
In the present paper, we consider the Cauchy problem of nonhomogeneous heat
conducting Navier–Stokes equations in the whole space $${\mathbb {R}}^2$$ .
Combining delicate energy estimates and a logarithmic interpolation inequality,
we derive the global existence and uniqueness of strong solutions. In
particular, the initial data can be arbitrarily large....
Isoperimetric Comparisons via Viscosity
The Journal of Geometric Analysis - Tập 26 - Trang 2831-2841 - 2015
Viscosity solutions are suitable notions in the study of nonlinear PDEs
justified by estimates established via the maximum principle or the comparison
principle. Here we prove that the isoperimetric profile functions of Riemannian
manifolds with Ricci lower bound are viscosity supersolutions of some nonlinear
differential equations. From these one can derive the isoperimetric inequalities
of Lévy-...
Effective Transitive Actions of the Unitary Group on Quotients of Hopf Manifolds
The Journal of Geometric Analysis - Tập 27 - Trang 1914-1919 - 2016
In our joint article with N. Kruzhilin of 2002, we showed that every connected
complex manifold of dimension $$n\ge 2$$ that admits an effective transitive
action by holomorphic transformations of the unitary group $$\mathop {\text
{U}}\nolimits _n$$ is biholomorphic to the quotient of a Hopf manifold by the
action of $${\mathbb Z}_m$$ for some integer m satisfying $$(n,m)=1$$ . In this
note, we c...
Energy Stability for a Class of Semilinear Elliptic Problems
The Journal of Geometric Analysis - - 2024
AbstractIn this paper, we consider semilinear elliptic problems in a bounded
domain $$\Omega $$ Ω contained in a given unbounded Lipschitz domain $${\mathcal
{C}} \subset {\mathbb {R}}^N$$ C ⊂ R N . Our aim is to study how the energy of a
solution behaves with respect to volume-preserving variations of the domain
$$\Omega $$ Ω inside $${\mathcal {C}}$$ C . Once a rigorous variational approach
to t...
on stability criterion of complete intersections
The Journal of Geometric Analysis - Tập 14 - Trang 533-544 - 2004
For protective varieties, it is known that Chow stable implies N-th
Hilbert-Mumford stable for N sufficiently large, which follows from the works of
J. Fogarty [2, 6]. In this article, we firstly shall provide a simple criterion
for Chow stability of complete intersections. The criterion for Chow stability
was previously provided by Mumford [5], but our calculation is different from
Mumford’s in t...
Complete algebraic vector fields on affine surfaces, Part I
The Journal of Geometric Analysis - Tập 13 - Trang 669-696 - 2003
In this work we study the singularities at infinity of algebraic vector fields
in dimension 2.These singularities will be classified under a mild assumption.
The general problem is also reduced to the study of the combinatorics of certain
resolutions which will be developed in Part II. Our main results are local and
therefore can be carried over more general surfaces. Whereas we deal with ℂ
-compl...
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...
A New Quaternion Hyper-Complex Space with Hyper Argument and Basic Functions via Quaternion Dynamic Equations
The Journal of Geometric Analysis - - 2022
On the Curvature of the Bismut Connection: Bismut–Yamabe Problem and Calabi–Yau with Torsion Metrics
The Journal of Geometric Analysis - Tập 33 - Trang 1-23 - 2023
We study two natural problems concerning the scalar and the Ricci curvatures of
the Bismut connection. Firstly, we study an analog of the Yamabe problem for
Hermitian manifolds related to the Bismut scalar curvature, proving that, fixed
a conformal Hermitian structure on a compact complex manifold, there exists a
metric with constant Bismut scalar curvature in that class when the expected
constant...
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