相关论文: On Gagliardo-Nirenberg Inequalities with vanishing…

Motivated by the study of trilinear forms for complex representations, we investigate the space of $G$-invariant linear forms on tensor products of irreducible admissible representations of $G = \mathrm{GL}_2(\mathbb{Q}_p)$ over…

We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, aswell as a weighted sharp trace Sobolev inequality on epigraphs of convex functions. This is done by using a generalized Borell-Brascamp-Lieb inequality,…

In this article, we prove a weighted Hardy inequality for $1<p<+\infty$ and dimension $d\ge1$. If $p>d$, then we can deduce from our weighted Hardy inequality a Poincar\'e inequality. The proof of the weighted Hardy inequality is based on…

We study fundamental forms of algebraic varieties using the sheaves of principal parts of line bundles and establish a vanishing theorem for any order fundamental forms. We also give connection of fundamental forms with the higher order…

We propose a new Borell-Brascamp-Lieb inequality which leads to novel sharp Euclidean inequalities such as Gagliardo-Nirenberg-Sobolev inequalities in R^n and in the half-space R^n\_+. This gives a new bridge between the geometric pont of…

We obtain a full characterization of Einstein-Maxwell $p$-form solutions $(\boldsymbol{g},\boldsymbol{F})$ in $D$-dimensions for which all higher-order corrections vanish identically. These thus simultaneously solve a large class of…

We prove optimality of the Gagliardo-Nirenberg inequality $$ \|\nabla u\|_{X}\lesssim\|\nabla^2 u\|_Y^{1/2}\|u\|_Z^{1/2}, $$ where $Y, Z$ are rearrangement invariant Banach function spaces and $X=Y^{1/2}Z^{1/2}$ is the…

We prove the factoriality of the following nodal threefolds: a complete intersection of hypersurfaces $F$ and $G\subset\mathbb{P}^{5}$ of degree $n$ and $k$ respectively, where $G$ is smooth, $|\mathrm{Sing}(F\cap…

Global and local weighted Gagliardo-Nirenberg inequalities with doubling measures are established. These inequalities are key ingredients for the regularity theory and existence of strong solutions for strongly coupled parabolic and…

Using Fourier analysis, we derive Wirtinger-type inequalities of arbitrary high order. As applications, we prove various sharp geometric inequalities for closed curves on the Euclidean plane. In particular, we obtain both sharp lower and…

We obtain sharp Hardy inequalities on antisymmetric functions where antisymmetry is understood for multi-dimensional particles. Partially it is an extension of the previously published paper \cite{HL}, where Hardy's inequalities were…

This paper has two parts. We first survey recent efforts on the Bloom conjecture which still remains open in the case of complex dimension at least 4. Bloom's conjecture concerns the equivalence of three regular types. There is a more…

We prove Grauert-Riemenschneider-type vanishing theorems for excellent dlt threefolds pairs whose closed points have perfect residue fields of positive characteristic $p>5$. Then we discuss applications to dlt singularities and to Mori…

We define a notion of general uniform interpolant, generalizing the notions of cover and of uniform interpolant and identify situations in which symbol elimination can be used for computing general uniform interpolants. We investigate the…

In this paper we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field K.

We study the nonlinear eigenvalue problem for the p-Laplacian, and more general problem constituting the Fucik spectrum. We are interested in some vanishing properties of sign changing solutions to these problems. Our method is applicable…

In this article, a proof of the interpolation inequality along geodesics in $p$-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel-Brascamp-Lieb inequality for general Riemannian and…

A classical result of N. Levinson characterizes the existence of a nonzero integrable function vanishing on a nonempty open subset of the real line in terms of the pointwise decay of its Fourier transform. We prove an analogue of this…

In this paper, we show several vanishing type theorems for $p$-harmonic $\ell$-forms on Riemannian manifolds ($p\geq2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of ${N}^{n+m}$ with flat normal bundle, we…

We prove a "strong" Durfee-type inequality for isolated hypersurface surface singularities, which implies Durfee's strong conjecture for such singularities with non-negative topological Euler number of the exceptional set of the minimal…