Related papers: p-lck with potential structure on LVMB manifolds

We show that a topological symplectic manifold has a canonically associated bi-Lipschitz structure. As a corollary, we obtain the first examples of non-existence and non-uniqueness for topological symplectic structures. Our arguments hold…

Let $(M^n, h)$ be a compact Hermitian manifold. Suppose $\lambda$ is the lowest eigenvalue of the complex Laplacian on $M$. We prove that $\lambda \geq C$ where $C$ depends only on the dimension $n$, the diameter $d$, the Ricci curvature of…

Let $L$ be a closed totally real submanifold of $\mathbb{C}^{n}$, $n\ge 2$, which is not Lagrangian. We observe that small enough tubular neighborhoods of $L$ give exotic examples of weak fillings of $ST^{\ast}L$ endowed with its standard…

We strongly believe that in order to prove two important geometrical pro\-blems in convexity, namely, the G. Bianchi and P. Gruber's Conjecture \cite{bigru} and the J. A. Barker and D. G. Larman's Conjecture \cite{Barker}, it is necessary…

Let M^3 be a compact, oriented, irreducible, and boundary incompressible 3-manifold. Assume that its fundamental group is without rank two abelian subgroups and its boundary is non-empty. We will show that every homomorphism from pi_1(M) to…

We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric…

We study the problem of determining all connected Lie groups $G$ which have the following property (hlp): every sub-Laplacian $L$ on $G$ is of holomorphic $L^p$-type for $1\leq p<\infty, p\ne 2.$ First we show that semi-simple non-compact…

A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…

It was conjectured by Bott-Grove-Halperin that a compact simply connected Riemannian manifold $M$ with nonnegative sectional curvature is rationally elliptic. We confirm this conjecture under the stronger assumption that $M$ has entire…

The paper focuses on the $L^{p}$-Positivity Preservation property ($L^{p}$-PP for short) on a Riemannian manifold $(M,g)$. It states that any $L^p$ function $u$ with $1<p<+\infty$, which solves $(-\Delta + 1)u\ge 0$ on $M$ in the sense of…

Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials…

The Hopf-Galois structures on normal extensions $K/k$ with $G=Gal(K/k)$ are in one-to-one correspondence with the set of regular subgroups $N\leq B=Perm(G)$ that are normalized by the left regular representation $\lambda(G)\leq B$. Each…

Let (M,I, \omega, \Omega) be a nearly Kaehler 6-manifold, that is, an SU(3)-manifold with the (3,0)-form \Omega and the Hermitian form \omega which satisfies $d\omega=3\lambda\Re\Omega, d\Im\Omega=-2\lambda\omega^2$, for a non-zero real…

Let $p$ be a prime number and $K$ a finite extension of $\mathbb{Q}_p$. We state conjectures on the smooth representations of $\mathrm{GL}_n(K)$ that occur in spaces of mod $p$ automorphic forms (for compact unitary groups). In particular,…

We construct covariant $q$-deformed holomorphic structures for all finitely-generated relative Hopf modules over the irreducible quantum flag manifolds endowed with their Heckenberger--Kolb calculi. In the classical limit these reduce to…

The $p$-adic Littlewood Conjecture due to De Mathan and Teuli\'e asserts that for any prime number $p$ and any real number $\alpha$, the equation $$\inf_{|m|\ge 1} |m|\cdot |m|_p\cdot |\langle m\alpha \rangle|\, =\, 0 $$ holds. Here, $|m|$…

Let $P_{\lambda\Sigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $\lambda$ of the standard symplex $\Sigma_n \subset \mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold…

Let $M$ be a connected, closed, oriented three-manifold and $K$, $L$ two rationally null-homologous oriented simple closed curves in $M$. We give an explicit algorithm for computing the linking number between $K$ and $L$ in terms of a…

Compact K\"ahler manifolds classically satisfy the Hard Lefschetz Theorem, which gives strong control on the underlying topology of the manifold. One expects a similar theorem to be true for K\"ahler Lie Algebroids, and we show for a…

LVM and LVMB manifolds are a large family of examples of non kahler manifolds. For instance, Hopf manifolds and Calabi-Eckmann manifolds can be seen as LVMB manifolds. The LVM manifolds have a very natural action of the real torus and the…