arXiv research

Proves non-vanishing CMC flux for specific manifolds.

Using the Bryant representation, we define a new flux on homology classes of CMC-1 surfaces in hyperbolic 3-space, satisfying a balancing formula which is useful to show nonexistencd of certain kinds of complete CMC-1 surfaces.

We construct higher genus Riemann's minimal surfaces properly embedded in the Euclidean space. To do that we glue end by end a Costa-Hoffman-Meeks examples to two halves genus zero Riemann's minimal surfaces. In first we need to perform a deformation of a Costa-Hoffman-Meeks example to prescribe the flux vector along t…

Bayesian analysis uncovers flux couplings in metabolic networks.

In $\mathbb{S}^2 \times \mathbb{R}$ there is a two-parameter family of properly embedded minimal annuli foliated by circles. In this paper we show that this family contains all properly embedded minimal annuli. We use the description of minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ by periodic harmonic maps $G : \…

Study introduces a probabilistic framework for air-sea fluxes using neural networks.

In this paper, we introduce a non linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry. As an application we construct unstable CMC spheres and outlying CMC spheres in asymptotically Schwarzschild manifolds with metrics like $g_{ij}=(1+\frac{1}{l})^{2}δ_{ij}+O(l^{-2})$. The existence of uns…

Unified description of fluxes and T-duality via symplectic manifolds.

New CMC surfaces with dihedral symmetry constructed from Darboux transforms.

Derives fluxes in M-theory compactifications and connects them to threebrane sigma-models.

11D supergravity completes with quantized C-field flux.

Analyzes quantization of flux observables in gauge theories.

We study the flux homomorphism for closed forms of arbitrary degree, with special emphasis on volume forms and on symplectic forms. The volume flux group is an invariant of the underlying manifold, whose non-vanishing implies that the manifold resembles one with a circle action with homologically essential orbits.

No proper biharmonic CMC compact hypersurface in a specific warped product space.

We propose an extension of the structure equation for constant mean curvature (CMC) surfaces in a three dimensional Riemannian space form to the associated CMC hierarchy of evolution equations by the higher-order commuting symmetries. Via the canonical formal Killing field, considered as an infinitely prolonged and loo…

M5-branes' flux quantization linked to non-abelian cohomology.

Study on Euler class and flux homomorphisms for non-orientable surfaces.

It is known that the topological T-duality exchanges $H$ and $F$-fluxes. In this paper, we reformulate the topological T-duality as an exchange of two Lie algebroids in the generalized tangent bundle. Then, we apply the same formulation to the Poisson-generalized geometry, which is introduced in arXiv:1408.2649 to defi…

FLUXtrapolation benchmarks machine learning for extrapolating ecosystem fluxes under distribution shifts.

Combines machine learning and convex limiting for accurate subgrid flux modeling in shallow-water equations.

Constructs cmc doublings of minimal surfaces via min-max theory.

We compute the flux of Killing fields through ends of constant mean curvature 1 in hyperbolic space, and we prove a result conjectured by Rossman, Umehara and Yamada : the flux matrix they have defined is equivalent to the flux of Killing fields. We next give a geometric description of embedded ends of finite total cur…

New method for flux quantization on phase space stacks.

New correspondence links fluxless to fluxy flag manifolds via T-duality.

We translate a classification scheme for periodic CMC surfaces developed by J. Dorfmeister and the author to discrete CMC surfaces in the sense of A. Bobenko and U. Pinkall. The scheme uses the dressing action on discrete CMC surfaces to arrive at a classification for periodic discrete CMC surfaces.

Paper studies flows of spinor fields with flux for unified theories.

Compactness proven for CMC surfaces with bounded topology and boundary length.

New cosmological spacetimes without CMC Cauchy surfaces found.

Unique CMC foliation in Minkowski space solved.

Machine learning and deep learning infer surface/groundwater exchange from temperature data.

Study on flux homomorphism and its extension in symplectic group of a disk.

Modernizes higher-dimensional supergravity, linking it to flux quantization.

Study singularities of CMC 1 surfaces in de Sitter space.

Invariant $r^\sharp$ predicts H-flux behavior under T-duality.

Survey on CMC surfaces in homogeneous 3-manifolds.

Proves existence and uniqueness of CMC foliations in cuspidal manifolds.

Estimates bandwidth for CMC initial data sets.

Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces established.

The paper explores CMC hypersurfaces in spheres, verifying Yau's conjecture.

Authors review CMC spacelike hypersurfaces and new existence results.

Study finds existence and non-existence of large stable CMC spheres in asymptotically flat 3-manifolds.

On a closed symplectic surface Sigma of genus two or more, we give a new construction of an extended flux map (a crossed homomorphism from the symplectomorphism group Symp(Sigma) to the cohomology group H^1(Sigma;R) that extends the flux homomorphism). This construction uses the topology of the Jacobian of the surface …

New mathematical framework connects M-theory charges to stable homotopy groups.

New CMC existence result for expanding cosmological spacetimes.

Python tool for constructing CMC surfaces using DPW method.

In this paper we numerically construct CMC deformations of the Lawson minimal surfaces $ξ_{g,1}$ using a spectral curve and a DPW approach to CMC surfaces in spaceforms.

A novel gravity theory based on Poisson Generalized Geometry is investigated. A gravity theory on a Poisson manifold equipped with a Riemannian metric is constructed from a contravariant version of the Levi-Civita connection, which is based on the Lie algebroid of a Poisson manifold. Then, we show that in Poisson Gener…

For a complete minimal surface in the Euclidean 3-space, the so-called flux vector corresponds to each end. The flux vectors are balanced, i.e., the sum of those over all ends are zero. Consider the following inverse problem: For each balanced n vectors, find an n-end catenoid which attains given vectors as flux. Here,…