Related papers: A Semi-Orthogonal Decomposition Theorem for Weight…
In 2019, Abramovich--Temkin--Wlodarczyk and McQuillan used weighted blow-ups to obtain very fast and functorial algorithms for resolution of singularities in characteristic zero. Recently, Abramovich--Quek--Schober simplified the…
We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schr\"odinger equation $i\partial_t u + \Delta u + |u|^{p-1}u=0$ on $\mathbf{R}^d$, close to the mass critical case and for any space…
We transfer the lower semi-continuity of Siegel disks with fixed Brjuno type rotation numbers to geometric limits. Here, we restrict to Lavaurs maps associated to quadratic polynomials with a parabolic fixed point.
The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case…
Stack-theoretic blow-ups have proven to be efficient in resolving singularities over fields of characteristic zero. In this article, we move forward towards positive characteristic where new challenges arise. In particular, the dimension of…
We extend the slow blow up solutions of Krieger, Schlag, and Tataru to semilinear wave equations on a curved background. In particular, for a class of manifolds $(M,g)$ we show the existence of a family of blow-up solutions with finite…
The study of nonlinear waves that collapse in finite time is a theme of universal interest, e.g. within optical, atomic, plasma physics, and nonlinear dynamics. Here we revisit the quintessential example of the nonlinear Schrodinger…
We consider the higher-order semilinear parabolic equation $$ \partial_t u = -(-\Delta)^{m} u + u|u|^{p-1}, $$ in the whole space $\mathbb{R}^N$, where $p > 1$ and $m \geq 1$ is an odd integer. We exhibit type I non self-similar blowup…
The Skorokhod reflection of a continuous semimartingale is unfolded, in a possibly skewed manner, into another continuous semimartingale on an enlarged probability space according to the excursion-theoretic methodology of Prokaj (2009).…
We investigate the natural involutive structure on the blow-up of ${\Bbb R}^n$ in ${\Bbb C}^n$ extending the complex structure on the complement of the exceptional hypersurface. Our main result is that this structure is hypocomplex, meaning…
We use standard constructions in algebraic geometry and homological algebra to extend the decomposition and hard Lefschetz theorems of T. Mochizuki and C. Sabbah so that they remains valid without the quasi-projectivity assumptions.
We give in this note a weighted version of Brianchon-Gram's decomposition for a simple polytope. This weighted version is a direct consequence of the ordinary Brianchon-Gram formula.
In this work, we consider a class of second order uniformly elliptic operators with smooth and bounded coefficients. We provide some estimates on the norm of the semigroup generated by these operators acting on weighted Sobolev spaces,…
We study orthogonal decompositions of symmetric and ordinary tensors using methods from linear algebra. For the field of real numbers we show that the sets of decomposable tensors can be defined be equations of degree 2. This gives a new…
In this paper we perform a refined blow up analysis of finite energy approximated solutions to a Nirenberg type problem on half spheres. The later consists of prescribing, under minimal boundary conditions, the scalar curvature to be a…
We consider in this paper a perturbation of the standard semilinear heat equation by a term involving the space derivative and a non-local term. We prove the existence of a blow-up solution, and give its blow-up profile. Our proof relies on…
We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence…
It is well known that the category of quasi-coherent sheaves on a gerbe banded by a diagonalizable group decomposes according to the characters of the group. We establish the corresponding decomposition of the unbounded derived category of…