Related papers: $L^p$-trace-free generalized Korn inequalities for…

We describe and characterize the contractively decomposable projections on noncommutative $\mathrm{L}^p$-spaces. Our result relies on a new lifting result for decomposable maps of independent interest and on some tools from ergodic theory.…

We construct a set of bounded vector fields dense in $L^p((0,2);W^{s,p}_{loc}(\mathbb{R}^2;\mathbb{R}^2))$ for $1\leq p <+\infty$ and $0\leq s<1$ with $p<1/s$ for which smooth regularisation of the vector field does not give a selection…

For a given Lipschitz domain $\Omega$, it is a classical result that the trace space of $W^{1,p}(\Omega)$ is $W^{1-1/p,p}(\partial\Omega)$, namely any $W^{1,p}(\Omega)$ function has a well-defined $W^{1-1/p,p}(\partial\Omega)$ trace on its…

We prove that all points of a toroidal compactification lying over 0-dimensional cusps are rationally equivalent in the integral Chow group for most classical modular varieties (Siegel, Hilbert, orthogonal, Hermitian, quaternionic). This…

Given n general points p_1, p_2,..., p_n \in P^r, it is natural to ask whether there is a curve of given degree d and genus g passing through them; by counting dimensions a natural conjecture is that such a curve exists if and only if \[n…

We prove an integral representation result for functionals with growth conditions which give coercivity on the space $SBD^p(\Omega)$, for $\Omega\subset\mathbb{R}^2$. The space $SBD^p$ of functions whose distributional strain is the sum of…

Let $E$ be an elliptic curve defined over $\mathbb{Q}$. For a quadratic number field $K$ and an odd prime number $p$, let $L$ be a $\mathbb{Z}_p$-extension of $K$. We prove that $E(L)_{\text{tors}}=E(K)_{\text{tors}}$ when $p>5$. It enables…

For a square-free integer $t$, Byeon \cite{byeon} proved the existence of infinitely many pairs of quadratic fields $\mathbb{Q}(\sqrt{D})$ and $\mathbb{Q}(\sqrt{tD})$ with $D > 0$ such that the class numbers of all of them are indivisible…

Let $f$ be a Hecke-Maass cusp form for $SL_3(\mathbb{Z})$ and $\chi$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^{\kappa}$ with $p$ prime and $\kappa\geq 10$. We prove a subconvexity bound $$…

In this work, we prove the $L^3$-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy…

In this paper, we verify the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension for $p\in[1,\infty)$. We also show that the $K$-theory of $L^p$ Roe algebras are independent of $p\in(1,\infty)$ for spaces with…

Let (C, p_1, p_2, \ldots, p_n) be a general marked curve of genus g, and q_1, q_2, ..., q_n \in P^r be a general collection of points. We determine when there exists a nondegenerate degree d map f : C \to P^r so that f(p_i) = q_i for all i.…

Let $(\lambda_n)_{n \geq 1}$ be a non-negative sequence with $\lambda_1>0$ and let $\Lambda_n=\sum^n_{i=1}\lambda_i$. We study the following Copson inequality for $0<p<1$, $L>p$, \begin{align*} \sum^{\infty}_{n=1}\left (\frac 1{\Lambda_n}…

We study trace inequalities of the type $$ \| T_k f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d\sigma)}, \qquad f \in L^p(d\sigma), $$ in the ``upper triangle case'' $1 \leq q<p$ for integral operators $T_k$ with positive kernels, where $d\sigma$ and…

Fix a number field $k$, integers $\ell, n \geq 2$, and a prime $p$. For all $r \geq 1$, we prove strong unconditional upper bounds on the $r$-th moment of $\ell$-torsion in the ideal class groups of degree $p$ extensions of $k$ and of…

We construct, for $p>n$, a concrete example of a complete non-compact $n$-dimensional Riemannian manifold of positive sectional curvature which does not support any $L^p$-Calder\'on-Zygmund inequality: \[ \forall\,\varphi\in…

Let E/k(T) be an elliptic curve defined over a rational function field of characteristic zero. Fix a Weierstrass equation for E. For points R in E(k(T)), write x_R=A_R/D_R^2 with relatively prime polynomials A_R(T) and D_R(T) in k[T]. The…

We prove that $p$-primary cohomology classes of a torus $T$ over a global function field of characteristic $p$ may be split by suitable separable $p$-primary extensions. More precisely, we show that such cohomology classes will split in any…

We investigate variable coefficient analogs of a recent work of Bortz, Hofmann, Martell and Nystr\"om [BHMN25]. In particular, we show that if $\Omega$ is the region above the graph of a Lip(1,1/2) (parabolic Lipschitz) function and $L$ is…

We obtain dimension-free concentration inequalities for $\ell^p$-norms, $p\geq2$, of infinitely divisible random vectors with independent coordinates and finite exponential moments. Besides such norms, the methods and results extend to some…