arXiv research

The study predicts solar flare productivity using magnetic data from SDO/HMI.

We conduct a post hoc analysis of solar flare predictions made by a Long Short Term Memory (LSTM) model employing data in the form of Space-weather HMI Active Region Patches (SHARP) parameters calculated from data in proximity to the magnetic polarity inversion line where the flares originate. We train the the LSTM mod…

Suppose M is a noncompact connected n-manifold and m is a good Radon measure of M with m(bdry M) = 0. Let H(M; m) denote the group of m-preserving homeomorphisms of M equipped with the compact-open topology and H_E(M; m) denote the subgroup consisting of all h in H(M; m) which fix the ends of M. Each h in H_E(M; m) mov…

For a non-compact n-manifold M let H(M) denote the group of homeomorphisms of M endowed with the Whitney topology and H_c(M) the subgroup of H(M) consisting of homeomorphisms with compact support. It is shown that the group H_c(M) is locally contractible and the identity component H_0(M) of H(M) is an open normal subgr…

Suppose M is a noncompact connected 2-manifold and m is a good Radon measure of M with m(partial M) = 0. Let H(M)_0 denote the identity component of the group of homeomorphisms of M equipped with the compact-open topology and let H(M; m)_0 denote the identity component of the subgroup consisting of m-preserving homeomo…

We prove that for any open orientable surface $S$ of finite topology, there exist a Riemann surface $\mathcal{M},$ a relatively compact domain $M\subset\mathcal{M}$ and a continuous map $X:\bar{M}\to\mathbb{C}^3$ such that: $\mathcal{M}$ and $M$ are homeomorphic to $S,$ $\mathcal{M}-M$ and $\mathcal{M}-\bar{M}$ contain…

Let $(Γ,γ)$ be a crystallization of connected compact 3-manifold $M$ with $h$ boundary components. Let $\mathcal{G}(M)$ and $\mathit k (M)$ be the regular genus and gem-complexity of $M$ respectively, and let $\mathcal{G}(\partial M)$ be the regular genus of $\partial M$. We prove that $$\mathit k (M)\geq 3 (\mathcal{G…

Suppose M is a noncompact connected oriented C^infty n-manifold and omega is a positive volume form on M. Let D^+(M) denote the group of orientation preserving diffeomorphisms of M endowed with the compact-open C^infty topology and D(M; omega) denote the subgroup of omega-preserving diffeomorphisms of M. In this paper …

Suppose that $M$ is a connected orientable $n$-dimensional manifold and $m>2n$. If $H^i(M,\R)=0$ for $i>0$, it is proved that for each $m$ there is a monomorphism $H^m(W_n,\on{O}(n))\to H^m_{\on{cont}}(\on{Diff}M,\R)$. If $M$ is closed and oriented, it is proved that for each $m$ there is a monomorphism $H^m(W_n,\on{O}…

Let $M_1$ and $M_2$ be orientable irreducible 3--manifolds with connected boundary and suppose $\partial M_1\cong\partial M_2$. Let $M$ be a closed 3--manifold obtained by gluing $M_1$ to $M_2$ along the boundary. We show that if the gluing homeomorphism is sufficiently complicated, then $M$ is not homeomorphic to $S^3…

Let $M$ be a surface sum of 3-manifolds $M_1$ and $M_2$ along a bounded connected surface $F$ and $\partial_i$ be the component of $\partial M_i$ containing $F$. If $M_i$ has a high distance Heegaard splitting, then any minimal Heegaard splitting of $M$ is the amalgamation of those of $M^1, M^2$ and $M^*$, where $M^i=M…

This paper encloses a complete and explicit description of the derivations of the Lie algebra D(M) of all linear differential operators of a smooth manifold M, of its Lie subalgebra D^1(M) of all linear first-order differential operators of M, and of the Poisson algebra S(M)=Pol(T*M) of all polynomial functions on T*M,…

For an $(m+1)$-dimensional space-time $(X^{m+1}, g),$ define a mapped null hypersurface to be a smooth map $ν:N^{m}\to X^{m+1}$ (that is not necessarily an immersion) such that there exists a smooth field of null lines along $ν$ that are both tangent and $g$-orthogonal to $ν.$ We study relations between mapped null hyp…

Let $x : M \to E^m$ be an isometric immersion of a Riemannian manifold $M$ into a Euclidean $m$-space. Denote by $Δ$ the Laplace operator of $M$. Then $Δ$ gives rise to a differentiable map $L :M \to E^m$, called the Laplace map, defined by $L(p)=(Δx)(p)$, $p\in M$. We call $L(M)$ the Laplace image, and the transformat…

Let $M$ be a regular Riemann surface with a metric which has constant scalar curvature $ρ$. We give the asymptotic expansion of the sum of the square norm of the sections of the pluricanonical bundles $K_{M}^{m}$. That is, \[\sum_{i=0}^{d_{m}-1}\|S_{i}(x_{0})\|_{h_{m}}^{2} \sim m(1+\fracρ{2 m})+O(e^{-\frac{(\log m)^{2}…

Let M be a closed connected manifold. Let m(M) be the Morse number of M, that is, the minimal number of critical points of a Morse function on M. Let N be a finite cover of M of degree d. M.Gromov posed the following question: what are the asymptotic properties of m(N) as d goes to infinity? In this paper we study the …

Study examines Yang-Mills-Higgs energy convergence to codimension-three area functional.

The Riemannian symmetric space SU_{2,m}/S(U_2U_m) is both Hermitian symmetric and quaternionic Kahler symmetric. Let M be a hypersurface in SU_{2,m}/S(U_2U_m) and denote by TM its tangent bundle. The complex structure of SU_{2,m}/S(U_2U_m) determines a maximal complex subbundle C of TM, and the quaternionic structure o…

New PL-invariants defined for 4-manifolds with boundary.

Let $M$ be a finite volume oriented Riemannian manifold of dimension $n\geq 3$ and curvature in $[-b^2,-1]$, with thick-thin decomposition $M=M(thick)\cup M(thin)$. Denote by $λ_k(M(thick))$ the k-th eigenvalue for the Laplacian on $M(thick)$, with Neumann boundary conditdions. We show that $λ_k(M(thick))/3\leq λ_k(M)$…

Let $\mathfrak{M}$ be the moduli space of torsion free $G_2$ structures on a compact 7-manifold $M$, and let $\mathfrak{M}_1 \subset \mathfrak{M}$ be the $G_2$ structures with volume($M$) $=1$. The cohomology map $π^3: \mathfrak{M} \to H^3(M, R)$ is known to be a local diffeomorphism. It is proved that every nonz…

Let $M$ be a complex manifold of dimension $n$ with smooth connected boundary $X$. Assume that $\overline M$ admits a holomorphic $S^1$-action preserving the boundary $X$ and the $S^1$-action is transversal on $X$. We show that the $\overline\partial$-Neumann Laplacian on $M$ is transversally elliptic and as a conseque…

Consider a compact Kähler manifold $M^m$ with Ricci curvature lower bound $Ric_M\geq -2(m+1) .$ Assume that its universal cover $$ has maximal bottom of spectrum $λ_1(\widetilde{M}$ Then we prove that $\widetilde{M}$ is isometric to the complex hyperbolic space $\Bbb{CH}^m.$

New Smith-Gysin sequence for non-semi-free actions without semi-free condition.

New invariant prevents minimal submanifolds in curved spaces.

The paper proves rigidity for certain product spaces and bounds for band widths.

Suppose M is a connected PL 2-manifold and X is a compact connected subpolyhedron of M (X \neq 1pt, a closed 2-manifold). Let E(X, M) denote the space of topological embeddings of X into M with the compact-open topology and let E(X, M)_0 denote the connected component of the inclusion i_X : X \subset M in E(X, M). In t…

If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M. We show that S(M_1 connect sum M_2) is isomorphic to S(M_1) tensor S(M_2) modulo torsion. In fact, we show that S(M_1 connect sum M_2) is isomorphic to S(M_1) tensot S(M_2) if we are working over a certain localized ring. We show the simila…

Let $Σ$ be a simply connected rational homology sphere. A pair of disjoint closed submanifolds $M_+, M_-$ in $Σ$ are called dual to each other if the complement $Σ- M_+$ strongly homotopy retracts onto $M_-$ or vice-versa. In this paper we will give a complete answer of which integral triples $(n; m_+, m_-)$ can appear…

Torus decomposition shows foliation detected slopes for glued knot manifolds.

New formula extracts full local information from ray transform data.

We use the notation EX(S>M), EXF(S>M) and DL(S>M), where M is a smooth manifold and S is a geometric structure. EX(S>M) is the question whether S exists in M. EXF(S>M) is the question whether M admits S-foliations. DL(S>M) is the search of an invariant measuring how M is far from admitting S. For many major geometric s…

In this paper we show that flat (m-1)-dimensional tori give nontrivial rational homology cycles in congruence covers of the locally symmetric space SL(m,Z) \SL(m,R)/SO(m). We also show that the dimension of the subspace of H_{m-1}(Γ\SL(m,R)/SO(m);Q) spanned by flat (m-1)-tori grows as one goes up in congruence covers.

We prove that if $M$ is a CW-complex and $*$ is a 0-cell of $M$, then the crossed module $Π_2(M,M^1,*)$ does not depend on the cellular decomposition of $M$ up to free products with $Π_2(D^2,S^1,*)$, where $M^1$ is the 1-skeleton of $M$. From this it follows that if $G$ is a finite crossed module and $M$ is finite, the…

In this paper, we prove a classification theorem for the stable compact minimal submanifolds of the Riemannian product of an $m_1$-dimensional ($m_1\geq3$) hypersurface $M_1$ in the Euclidean space and any Riemannian manifold $M_2$, when the sectional curvature $K_{M_1}$ of $M_1$ satisfies $\frac{1}{\sqrt{m_1-1}}\leq K…

Let M be a compact, connected non-orientable surface without boundary and of genus g greater than or equal to 3. We investigate the pure braid groups P_n(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 --> P_m(M {x_1,...,x_n}) --> P_{n+m}(M) --> P_n(M) --> 1, where m,n ar…

We construct, for $m\geq 6$ and $2n\leq m$, closed manifolds $M^{m}$ with finite nonzero $\varphi(M^{m},S^{n}$), where $\varphi(M,N)$ denotes the minimum number of critical points of a smooth map $M\to N$. We also give some explicit families of examples for even $m\geq 6, n=3$, taking advantage of the Lie group structu…

The space AH(M) of marked hyperbolic 3-manifold homotopy equivalent to a compact 3-manifold with boundary M sits inside the PSL_2(C)-character variety X(M) of π_1(M). We study the dynamics of the action of Out(π_1(M)) on both AH(M) and X(M). The nature of the dynamics reflects the topology of M. The quotient AI(M)=AH(M…

Let $FM,\mathcal{M}_M$ be the bundles of linear frames and Riemannian metrics of a manifold $M$, respectively. The existence of a unique $\mathrm{Diff}M$-invariant connection form on $J^1\mathcal{M}_M\times_MFM\to J^1\mathcal{M}_M$, which is Riemannian with respect to the universal metric on $J^1\mathcal{M}_M\times_MTM…

Gluck twists on spheres yield equivalent 4-manifolds under certain conditions.

Recently, Naghi et al. \cite{NAGHI} studied warped product skew CR-submanifold of the form $M_1\times_fM_\bot$ of order $1$ of a Kenmotsu manifold $\bar{M}$ such that $M_1=M_T\times M_θ$, where $M_T$, $M_\bot$ and $M_θ$ are invariant, anti-invariant and proper slant submanifolds of $\bar{M}$. The present paper deals wi…

Let M^n be a compact n-dimensional principal T^k-bundle. We consider collapsings of M on N=M/T^k such that the diameter and sectional curvature of M satisfy diam(M)<d and |K(M)|<a, and give examples of collapsings for all k such that the first non-zero eigenvalue of Laplacian acting on 1-forms and 2-forms of M are boun…

In this paper, we study $n$-dimensional hypersurfaces with constant $m^{\text{th}}$ mean curvature $H_m$ in a unit sphere $S^{n+1}(1)$ and prove that if the $m^{\text{th}}$ mean curvature $H_m$ takes value between $\dfrac{1}{(\tan \fracπ{k})^m}$ and $\frac{k^2-2}{n}(\frac{k^2+m-2}{n-m})^{\frac{m-2}{2}}$ for $1\leq m\le…

The sigma invariant is studied for torus, K3 surface, and 3d manifolds.

We consider a compact, oriented, smooth Riemannian manifold $M$ (with or without boundary) and we suppose $G$ is a torus acting by isometries on $M$. Given $X$ in the Lie algebra and corresponding vector field $X_M$ on $M$, one defines Witten's inhomogeneous coboundary operator $d_{X_M} = d+ι_{X_M}: Ω_G^\pm \toΩ_G^\mp$…

We consider maximum solution $g(t)$, $t\in [0, +\infty)$, to the normalized Ricci flow. Among other things, we prove that, if $(M, ω)$ is a smooth compact symplectic 4-manifold such that $b_2^+(M)>1$ and let $g(t),t\in[0,\infty)$, be a solution to (1.3) on $M$ whose Ricci curvature satisfies that $|\text{Ric}(g(t))|\l…

We give a new proof of the classification of contact real hypersurfaces with constant mean curvature in the complex hyperbolic quadric ${Q^m}^* = SO_{m,2}^o/SO_mSO_2$, where $m\geq 3$. We show that a contact real hypersurface $M$ in ${Q^m}^*$ for $m\geq 3$ is locally congruent to a tube of radius $r{\in}{\mathbb R}^+$ …

We prove that on any compact manifold $M^n$ with boundary, there exist a conformal class $C$ such that for any riemannian metric $g\in C$, $λ_1(M^n,g)Vol(M^n,g)^{2/n}< n.Vol(S^n,g_{\textrm{can}})^{2/n}$ and $σ_1(M,g,ρ)\mathcal M(\partial M)Vol(M)^{\frac{2-n}n}<n.Vol(S^n,g_{\textrm{can}})^{2/n}$, where $λ_1(M^n,g)$ deno…