arXiv research

Paper proves constants for Moser-Trudinger inequality on surfaces.

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

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.

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

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

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…

Kuranishi's proof of complex deformation theory revisited

We prove a stability result for volume forms on fiber bundles with compact base and noncompact fibers. This generalizes the classical results of Moser and Greene--Shiohama, and recent work by the authors.

New theorems prove uniqueness of solutions to geometric PDEs.

The abstract proves a Moser-like theorem for C-symplectic structures and applies it to complex manifolds.

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…

Theorems adapted for prequantum systems, showing symplectomorphism and gauge transformation.

We prove the conjecture of Tian on the strong form of the Moser-Trudinger inequality for Kahler-Einstein manifolds with positive first Chern class, when there are no holomorphic vector fields, and, more generally, when the setting is invariant under a maximal compact subgroup of the automorphism group.

New inequality criterion for a mean field equation on spheres.

In [16], we established Trudinger-Moser inequalities for complete noncompact Riemannian manifold on which the Ricci curvature has lower bound and the injectivity radius is strictly positive. In this note, we improve those inequalties when the manifold is the hyperbolic space. The method we used here is still gluing loc…

We reconsider the (rational) Calogero-Moser system from the point of view of bi-Hamiltonian geometry. By using geometrical tools of the latter, we explicitly construct set(s) of spectral canonical coordinates, that is, complete sets of Darboux coordinates defined by the eigenvalues and the eigenvectors of the Lax matri…

This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We motivate the definition of weak equivalence (found in the literature) by studying diff…

We show how the classical Moser Lemma from symplectic geometry extends to generalized complex structures (GCS) on arbitrary Courant algebroids. For this, we extend the notion of Lie derivative to sections of the tensor bundle $(\otimes^i E)\otimes(\otimes^j E^*)$ with respect to sections of the Courant algebroid $E$ us…

Paper develops a weighted linearization approach for vector fields.

Researchers found counterexamples to a 2-jet determination theorem in higher codimension.

Researchers solve a Riemannian geometry problem using warped products.

The paper proves a Moser-Trudinger inequality for zero-mean functions in 2D.

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

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

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 …

Note on advancements in nonlinear elliptic equations' regularity theory.

Sharp heat kernel and Green's function estimates on Euclidean volume growth manifolds.

We verify a conjecture of Gillet-Soulé. We prove that the determinant of the Laplacian on a line bundle over $\mathbb{CP}^{1}$ is always bounded from above. This can also be viewed as a multi-particle generalization of the Moser-Trudinger Inequality. Furthermore, we conjecture that this functional achieves its maximum …

Gradient estimates for special harmonic functions on manifolds.

The paper proves symplectic neighbourhood theorems for stratified subspaces.

A classical result of Aubin states that the constant in Moser-Trudinger-Onofri inequality on $\mathbb{S}^{2}$ can be imporved for furnctions with zero first order moments of the area element. We generalize it to higher order moments case. These new inequalities bear similarity to a sequence of Lebedev-Milin type inequa…

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

We study the general $J$-flows. We use Moser iteration to obtain the uniform estimate.

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…

Second part of proving linearization theorem for sl2(C).

The paper explores similarities in even and odd-dimensional geometry.

In this article, we first describe a normal form of real-analytic, Levi-nondegenerate submanifolds of $C^N$ of codimension d $\ge$ 1 under the action of formal biholomorphisms, that is, of perturbations of Levi-nondegenerate hyperquadrics. We give a sufficient condition on the formal normal form that ensures that the n…

Moser Flow generates models for complex geometries on manifolds without ODE solvers.

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…

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

Let $M^3 \subset \mathbb{C}^2$ be a $\mathcal{C}^ω$ Levi nondegenerate hypersurface. In the literature, Cartan-Moser chains are detected from rather advanced considerations: either from the construction of a Cartan connection associated with the CR equivalence problem; or from the construction of a formal or converging…

Describes geodesic scattering on hyperboloids using quadrics results.

The paper studies deformations of symplectic groupoids using cohomology and spectral sequences.

Uniform proof of Kähler-Einstein metrics with arbitrary polarizations.

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