arXiv research

Stability of Lie group homomorphisms and subgroups via Moser type argument.

In the first part of the paper we investigate some geometric features of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds. By exploring rearrangement arguments, isoperimetric estimates, and gluing local uniform estimates via Gromov's covering lemma, we provide a Coulhon, Saloff-Coste and Varopo…

We introduce the concept of G2(2)-structure on an orientable 3-manifold M using the setting of generalized geometry of type Bn, study their local deformation by making use of a Moser-type argument, and give a description of the cone of G2(2)-structures.

We give a local classification of generalized complex structures. About a point, a generalized complex structure is equivalent to a product of a symplectic manifold with a holomorphic Poisson manifold. We use a Nash-Moser type argument in the style of Conn's linearization theorem.

We derive the sharp Moser-Trudinger-Onofri inequalities on the standard $n$-sphere and CR $(2n+1)$- sphere as the limit of the sharp fractional Sobolev inequalities for all $n\ge 1$. On the $2$-sphere and $4$-sphere, this was established recently by S.-Y. Chang and F. Wang. Our proof uses an alternative and elementary …

The paper proves a Moser-Trudinger inequality on metric spaces with curvature-dimension conditions.

Study metric perturbations to make degenerate harmonic forms non-degenerate.

Study on deformations of Lie groupoid morphisms and their properties.

New theorems prove uniqueness of solutions to geometric PDEs.

Paper proves Liouville theorems for harmonic functions under specific curvature bounds.

Improved Moser-Trudinger-Onofri inequality with constraints on sphere.

The study offers conditions for Darboux charts on specific types of manifolds.

Study Betti numbers of manifolds converging to covers, deriving new convergence results.

The paper uses Nash-Moser iteration to prove gradient estimates for nonlinear equations on Riemannian manifolds.

We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamental properties of the deformation cohomology including Morita invariance…

We propose two constructions extending the Chern-Moser normal form to non-integrable Levi-nondegenerate (hypersurface type) almost CR structures. One of them translates the Chern-Moser normalization into pure intrinsic setting, whereas the other directly extends the (extrinsic) Chern-Moser normal form by allowing non-C…

Paper analyzes solutions to quasilinear elliptic equations on manifolds using Nash-Moser iteration.

This paper is about the rigidity of compact group actions in the Poisson context. The main resut is that Hamiltonian actions of compact semisimple type are rigid. We prove it via a Nash-Moser normal form theorem for closed subgroups of SCI-type. This Nash-Moser normal form has other applications to stability results th…

We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation argument. The passing to general orbits (Weinstein) is given a more conceptual inte…

Researchers solve a Riemannian geometry problem using warped products.

We prove Aubin's "Hypothese fondamentale" concerning the existence of Moser-Trudinger type inequalities on any integral compact Kähler manifold X. In the case of the anti-canonical class on a Fano manifold the constants in the inequalities are shown to only depend on the dimension of X (but there are counterexamples to…

Paper proves constants for Moser-Trudinger inequality on surfaces.

Uniform proof of Kähler-Einstein metrics with arbitrary polarizations.

The paper studies gradient estimates for solutions of a nonlinear elliptic equation on Riemannian manifolds.

We derive a Harnack inequality for positive solutions of the $f$-heat equation and Gaussian upper and lower bounds for the $f$-heat kernel on complete smooth metric measure spaces $(M, g, e^{-f}dv)$ with Bakry-Émery Ricci curvature bounded below. The lower bound is sharp. The main argument is the De Giorgi-Nash-Moser t…

Mabuchi introduced multiplier Hermitian structures on compact Kahler manifolds and defined metrics similar to Kahler-Einstein metrics under these structures. In this note we generalize the inequality of Moser-Trudinger type on Kahler-Einstein manifolds to this case.

Proves a theorem similar to Moser's using a normalization method.

We study the blow-up behaviour of minimizing sequences for the singular Moser-Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence o…

Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.

Establishes necessary and sufficient conditions for smooth triviality of Lie subalgebras and Lie ideals, and proves Moser's trick for foliations.

Moser's theorem (1965) states that the diffeomorphism group of a compact manifold acts transitively on the space of all smooth positive densities with fixed volume. Here we describe the extension of this result to manifolds with corners. In particular we obtain Moser's theorem on simplices. The proof is based on Banyag…

Sharp inequalities on curved spaces with bounded curvature.

Extends symplectic reduction and theorem to Lie algebroids.

In this paper, we show that the existence of Sasakian-Einstein metrics is closely related to the properness of corresponding energy functionals. Under the condition that admitting no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of Sasakian-Einstein metric implies a Moser-Trudinger type i…

The paper establishes gradient estimates and Liouville theorems for Φ-Laplacian equations on Riemannian manifolds.

The paper extends entropy concepts to Monge-Ampère measures with prescribed singularities.

There are proven few analogues of the Theorem of Moser using The Approximation Theorem of Artin.

Tian's conjectures solved in Kahler geometry, linking metrics and inequalities.

Develops new strategy for Hessian estimates in Lagrangian mean curvature equation.

Though Trudinger-Moser inequalities on compact Riemannian manifolds or Euclidean space are well understood, we know little about them on complete noncompact Riemannian manifolds. In this paper, we established respectively necessary condition and sufficient condition under which Trudinger-Moser inequalities hold on comp…

We prove a sharp Onofri-type inequality and non-existence of extremals for a Moser-Tudinger functional on the sphere in the presence of potentials having positive order singularities. We also investigate the existence of critical points and give some sufficient conditions under symmetry or nondegeneracy assumptions.

Kuranishi's proof of complex deformation theory revisited

A new direct construction method for Cartan-Moser chains.

Study finds solutions to nonlinear Schrödinger equation on finite graphs.

Constructs harmonic spinors and 1-forms on 3-manifold connected sums and torus sums.

Classifies singular solutions to Liouville equation with constant Q-curvature metrics.

We develop a variational calculus for a certain free energy functional on the space of all probability measures on a Kahler manifold X. This functional can be seen as a generalization of Mabuchi's K-energy functional and its twisted versions to more singular situations. Applications to Monge-Ampère equations of mean fi…

We prove a conjecture saying that complex projective space has maximal volume (degree) among all toric Kaehler-Einstein manifolds of dimension n. The proof is inspired by our recent work on sharp Moser-Trudinger and Brezis-Merle type inequalities for the complex Monge-Ampere operator, but is essentially self-contained.