Establishes necessary and sufficient conditions for smooth triviality of Lie subalgebras and Lie ideals, and proves Moser's trick for foliations.
problem Smooth triviality of Lie subalgebras and Lie ideals
method Establishing necessary and sufficient conditions and proving Moser's trick for foliations
result Direct proof of Moser's trick for foliations
Paper develops a weighted linearization approach for vector fields.
problem Linearizability of vector fields under weighted conditions.
method Formal Moser trick applied to power series, addressing weighted non-resonance condition.
result Formal Moser trick works over any field of characteristic zero.
The paper proves symplectic neighbourhood theorems for stratified subspaces.
problem Finding symplectic neighbourhoods of stratified subspaces.
method Analogy with Weinstein's neighbourhood theorem, strong version of Moser's trick, and tubular neighbourhood theorem.
result Generalization of existing constructions for exotic Lagrangians.
The paper explores similarities in even and odd-dimensional geometry.
problem Understanding the Lagrangian Grassmannian in cosymplectic geometry.
method Study of compatible co-complex structures, Moser's trick, and Weinstein 1-form derivation.
result The de Rham class of the Weinstein 1-form is a co-flux.
We provide sufficient conditions for the existence of Darboux charts on weakly symplectic bounded Fréchet manifolds by using the Moser's trick.
Two Morse-Bott volume forms are diffeomorphic if their cohomology classes are equal.
problem Establishing equivalence of Morse-Bott volume forms.
method Adapting Moser's trick to Morse-Bott volume forms.
result Two Morse-Bott volume forms with the same zero set are diffeomorphic if and only if they have equal total volumes.
We give a construction to obtain canonically an ``isotropic average'' of given C1-close isotropic submanifolds of a symplectic manifold. To do so we use an improvement of Weinstein's submanifold averaging theorem (obtained in collaboration with H. Karcher) and apply ``Moser's trick''. We also present an application …
Paper proves constants for Moser-Trudinger inequality on surfaces.
problem Establishing constants for Moser-Trudinger inequality on surfaces.
method Using systole, isoperimetric constant, and curvature as parameters.
result Constants can be chosen to depend on only 3 parameters.
Proves a theorem similar to Moser's using a normalization method.
problem Proving a theorem similar to Moser's in a specific context.
method Iterative normalization procedure based on Generalized Fischer Decompositions.
result An analogue of the Theorem of Moser proven.
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.
problem Establishing inequalities on curved spaces with curvature constraints.
method Using Sobolev and Moser-Trudinger inequalities on noncompact Riemannian manifolds with Ricci curvature bounded below.
result Best constants for inequalities on curved spaces with curvature constraints.
Extends symplectic reduction and theorem to Lie algebroids.
problem Symplectic reduction and theorem for Lie algebroids.
method Extends Marsden-Weinstein reduction and Darboux-Moser-Weinstein theorems.
result Obtained coisotropic embedding theorem for symplectic Lie algebroids.
We investigate when the Chevalley-Eilenberg differential of a complex Lie algebroid on a manifold with boundary admits a Hodge decomposition. We introduce the concepts of Cauchy-Riemann structures, elliptic and non-elliptic boundary points and Levi-forms, which we use to define the notion of q-convexity. We show that t…
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.
problem Proving a Moser-Trudinger inequality on metric measure spaces.
method Rearrangement of functions on CD(k,n)-spaces satisfying a Polya-Szegö type inequality.
result Characterization of manifolds with lower bounded Ricci curvature admitting a Moser-Trudinger inequality.
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
problem Existence of complex deformations on compact complex manifolds
method Hamilton-Nash-Moser implicit function theorem
result Revisits classical proof with modern tools
This is the first in a series of papers dedicated to the study of Poisson manifolds of compact types (PMCTs). This notion encompasses several classes of Poisson manifolds defined via properties of their symplectic integrations. In this first paper we establish some fundamental properties of PMCTs, which already show th…
A new direct construction method for Cartan-Moser chains.
problem Detecting Cartan-Moser chains from advanced considerations.
method Inspection of Lie prolongations of infinitesimal automorphisms.
result Found a simple cubic degenerate orbit locus.
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.
problem Proving uniqueness of solutions to geometric PDEs.
method Analyzing nonlinear elliptic PDEs of divergence form.
result Proved several Moser-Bernstein type theorems.
The abstract proves a Moser-like theorem for C-symplectic structures and applies it to complex manifolds.
problem Analyzing the isotopy of C-symplectic structures and their applications.
method Proves an analogue of Moser's isotopy theorem for families of C-symplectic structures.
result Locally trivial degenerate twistorial deformation over the base of holomorphic Lagrangian fibrations.
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.
problem Adapting classical theorems to prequantum systems.
method Establishing analogs of the Darboux, Moser, and Weinstein theorems.
result Prequantum systems with vanishing first cohomology are equivalent up to 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.
problem Finding uniqueness in a mean field equation on spheres.
method Established a new Moser-Trudinger-Onofri inequality with a constraint on moments deviation.
result A threshold for deviation is a uniqueness criterion for the mean field equation.
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…
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 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…
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 (⊗iE)⊗(⊗jE∗) with respect to sections of the Courant algebroid E us…
Researchers found counterexamples to a 2-jet determination theorem in higher codimension.
problem Counterexample construction to the 2-jet determination Chern-Moser Theorem in higher codimension.
method Constructed counterexamples of quadratic submanifolds with specific properties.
result Generated counterexamples to the 2-jet determination Chern-Moser Theorem in higher codimension.
Paper defines embolic volume and relates it to Betti number using the covering trick.
problem Relating embolic volume to topological invariants.
method Covering trick from systolic geometry applied to Berger's inequality.
result Relates embolic volume to the first Betti number.
Researchers solve a Riemannian geometry problem using warped products.
problem Solving a Moser-Bernstein problem in warped Riemannian manifolds.
method Study entire solutions to the minimal hypersurface equation in warped products.
result Solves the Moser-Bernstein problem in a broader class of Riemannian manifolds.
The paper proves a Moser-Trudinger inequality for zero-mean functions in 2D.
problem Proving a Moser-Trudinger inequality for zero-mean functions in 2D.
method Analyzing the supremum of a specific integral over functions in W1,2(Ω) with zero mean and bounded gradient norm. result The supremum is finite and can be attained for β∈(0,1), partially generalizing Chang and Yang's result. Study of skateboard flips as continuous curves in SO(3) group.
problem Characterize skateboard flip tricks as continuous motions.
method Model flips as curves in SO(3), analyze lifts to S3, derive formulas. result There are only four distinct flip tricks up to continuous deformation.
A new method centers outliers in robust PCA without manual intervention.
problem Outliers in robust PCA require manual centering, complicating the analysis.
method Introduces a 'bias trick' to automatically center non-outliers.
result First optimal RPCA algorithm with automatic centering.
Paper analyzes solutions to quasilinear elliptic equations on manifolds using Nash-Moser iteration.
problem Analyzing positive solutions to quasilinear elliptic equations on manifolds with bounded Ricci curvature.
method Employing Nash-Moser iteration technique to derive logarithmic gradient estimates and Liouville properties.
result Derives universal logarithmic gradient estimates for positive solutions under certain conditions.
Nash's theorem proved with Günther's trick
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
The paper uses Nash-Moser iteration to prove gradient estimates for nonlinear equations on Riemannian manifolds.
problem Proving gradient estimates for solutions of nonlinear equations on Riemannian manifolds.
method Employing Nash-Moser iteration technique to establish gradient estimates.
result Gradient estimates for solutions of nonlinear equations on Riemannian manifolds are proven.
Explains Conway's tangle trick and its mathematical origins.
problem Understanding the relationship between braids and elliptic curves.
method Discusses the tangle trick, its mathematical underpinnings, and historical context.
result Establishes the connection between braids and elliptic curves.
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≥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 …
Unified framework for gradient estimation in combinatorial spaces.
problem Scaling relaxed gradient estimators to large combinatorial distributions.
method Introducing stochastic softmax tricks within the perturbation model framework.
result Stochastic softmax tricks improve model performance and discover more latent structure.
Note on advancements in nonlinear elliptic equations' regularity theory.
problem Nonlinear elliptic equations and their regularity.
method De Giorgi-Nash-Moser theory, Krylov-Safonov theory, Evans-Safonov theory.
result Contributions to Hilbert's 19th problem and fully nonlinear equations.
We prove all knots can be transformed into a trefoil using special diagrams.
problem Transforming any knot into a trefoil using magic tricks.
method Introducing knotholder diagrams to encode transformations.
result All knots can be transformed into a trefoil.
Geometric trick simplifies link homotopy and concordance.
problem Homotopy and concordance of links in homology spheres.
method Relative Whitney trick to remove double points.
result Links in homology spheres can be simplified to topologically slice links.
Sharp heat kernel and Green's function estimates on Euclidean volume growth manifolds.
problem Estimating heat kernels and Green's functions on specific Riemannian manifolds.
method Analyzing noncompact Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth.
result Sharp Moser-Trudinger inequalities on manifolds with Euclidean volume growth.
Harmonic functions stable under small changes.
problem Stability of multivalued harmonic functions under deformations.
method Application of Nash-Moser implicit function theorem.
result Stability of harmonic sections under small deformations.
We verify a conjecture of Gillet-Soulé. We prove that the determinant of the Laplacian on a line bundle over CP1 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 …