arXiv research

Paper classifies transnormal systems on compact 3-manifolds.

Explicitly describes pluriclosed metrics on compact Lie groups.

Study global solutions for Boussinesq systems on curved manifolds.

The paper studies eigenvalues of a special Laplacian system on compact manifolds.

Study on electrostatic systems with boundary, proving new geometric inequalities.

New cohomology theory shows compact Lie group actions are Morita invariant.

We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.

Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that the underlying compact symmetry group acts in a polar manner in the sense that there exist regularly embedded, closed, connected submanifol…

Study confirms Chern's conjecture on compact Hessian manifolds and classifies their topologies.

We are concerned with the global weak continuity of the Cartan structural system -- or equivalently, the Gauss--Codazzi--Ricci system -- on semi-Riemannian manifolds with lower regularity. For this purpose, we first formulate and prove a geometric compensated compactness theorem on vector bundles over semi-Riemannian m…

In X-ray binary star systems consisting of a compact object that accretes material from an orbiting secondary star, there is no straightforward means to decide if the compact object is a black hole or a neutron star. To assist this classification, we develop a Bayesian statistical model that makes use of the fact that …

We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide a plethora of examples of Haar system preserving morphisms and discuss connecti…

The reduction of biharmonic maps equation in terms of the Maurer-Cartan form for all smooth map of any compact Riemannian manifolds into a compact Lie group with bi-invariant Riemannian metric is obtained. By this formula, all the biharmonic curves into a compact Lie group and all biharmonic maps from a 2-dimensional o…

Proves inequality linking function deviation to gradient norm on compact manifolds.

Sharp regularity for Pfaff system leads to isometric immersions in arbitrary dimensions.

The paper studies random systems of holomorphic sections on compact Kähler manifolds and proves equidistribution results.

GNMC reduces XCSF population size while preserving function approximation and policy accuracy.

Minimal energy local systems on curves are compact components of character varieties.

Bayesian neural network predicts planetary instability.

We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological invariants and the geometric and Lyapunov growths of these foliations. As an applicat…

New solutions to SU(n+1) Toda system found on compact Riemann surfaces with cone singularities.

We are interested in global properties of systems of left-invariant differential operators on compact Lie groups: regularity properties, properties on the closedness of the range and finite dimensionality of their cohomology spaces, when acting on various function spaces e.g. smooth, analytic and Gevrey. Extending the …

Study on fourth order Lamm-Riviere system for biharmonic mappings in 4D.

We classify the systems of $T$-roots of the flag manifolds $M$ of the exceptional compact simple Lie groups with the second Betti number $b_2(M)\ge2$.

Using the implicit function theorem, we prove existence of solutions of the so-called conformally covariant split system on compact 3-dimensional Riemannian manifolds. They give rise to non-Constant Mean Curvature (non-CMC) vacuum initial data for the Einstein equations. We investigate the conformally covariant split s…

The paper estimates variance of random sections on complex manifolds.

Study complex structures and curvature equations on compact manifolds.

We prove short-time existence for the Einstein-Euler-Entropy system for non-isentropic fluids with data in uniformly local Sobolev spaces. The cases of compact as well as non-compact Cauchy surfaces are covered. The method employed uses a Lagrangian description of the fluid flow which is based on techniques developed b…

For compact CR manifolds of hypersurface type which embed in complex projective space, we show that for all k large enough there exist linear systems of ${\mathcal{O}}(k)$ which when restricted to the CR manifold are generic in a suitable sense. These systems are constructed using approximately holomorphic geometry.

A weight system on graph homology was constructed by Rozansky and Witten using a compact hyperkähler manifold. A variation of this construction utilizing holomorphic vector bundles over the manifold gives a weight system on chord diagrams. We investigate these weights from the hyperkähler geometry point of view.

We establish the weak continuity of the Gauss-Coddazi-Ricci system for isometric embedding with respect to the uniform $L^p$-bounded solution sequence for $p>2$, which implies that the weak limit of the isometric embeddings of the manifold is still an isometric embedding. More generally, we establish a compensated comp…

Study the deformation theory of Einstein-Yang-Mills system on compact manifolds.

Deep learning detects arrhythmia from RR-interval ECG data.

The defining equations for Killing vector fields and conformal Killing vector fields are overdetermined systems of PDE. This makes it difficult to solve the systems numerically. We propose an approach which reduces the computation to the solution of a symmetric eigenvalue problem. The eigenvalue problem is then solved …

Study of motion control systems on Lie groups with specific geometric constraints.

A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.

New isometric solutions found for heterotic G2-system.

In this paper we construct explicit smooth solutions to the Strominger system on generalized Calabi-Gray manifolds, which are compact non-Kähler Calabi-Yau 3-folds with infinitely many distinct topological types and sets of Hodge numbers.

In this short note we extend Chow and Lu's advanced maximum principles for parabolic systems on closed manifolds to the case of compact manifolds with boundary, which also generalizes a Hopf type theorem of Pulemotov.

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of ana…

Deep neural nets approximate random dynamical system trajectories uniformly in time.

The space of the global sections of chiral de Rham complex on a compact Ricci-flat Kähler manifold is calculated and it is expressed as an invariant subspace of a $βγ-bc$ system under the action of certain Lie algebra.

The paper resolves compactness and non-compactness for fourth- and sixth-order Q-curvature problems.

Study stabilizes second-order systems to first-order dynamics.

We consider a system of coupled free boundary problems for pricing American put options with regime-switching. To solve this system, we first employ the logarithmic transformation to map the free boundary for each regime to multi-fixed intervals and then eliminate the first-order derivative in the transformed model by …

We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action - by the whole subgroup of loops which extend holomorphically to the exterior disc - on the $U$-hierarchy of the ZS-AKN…

A compactness theorem is proved for a family of Kähler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a splitting theorem and some rigidity theorems are proved for Einstein-Maxwell systems.

Classifies almost-toric systems in four dimensions.