Related papers: Finitude g\'eom\'etrique en g\'eom\'etrie de Hilbe…
This note contains a correction of the proofs of the main results of the paper [A. Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 (2005), 383-432]. The results are correct as originally stated.
The purpose of this erratum and addendum is to correct the errors in [1]. It consists of five components: 1. Lemma 7.1 and Proposition 7.2 are wrong and discarded; 2. A new proof of existence $\lambda(\xi)$ in (7.1) without Proposition 7.2;…
We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.
We amend the statement of point~(i) in Theorem~1.3 in arxiv:0901.1022 and supply the additional arguments and minor changes for the results that depend on it. We also seize the occasion and generalize to non-finitely generated lattices.
The First and Second Liouville's Theorems provide correspondingly criterium for integrability of elementary functions "in finite terms" and criterium for solvability of second order linear differential equations by quadratures. The…
We address two errors made in our paper arXiv:1511.03423. The most significant error is in Theorem 1.1. We repair this error, and show that the main result, Theorem 2.5 of arXiv:1511.03423, is true. The second error is in one of our…
This is an erratum to our paper.
This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.
This short note is an erratum to arXiv:1306.4304, correcting the proof of one of its main results. It includes some counterexamples regarding infinite-dimensional unipotent groups and affine spaces that may be of independent interest.
We survey recent contributions to finite element exterior calculus on manifolds and surfaces within a comprehensive formalism for the error analysis of vector-valued partial differential equations on manifolds. Our primary focus is on…
Over an algebraically closed field, various finiteness results are known regarding the automorphism group of a K3 surface and the action of the automorphisms on the Picard lattice. We formulate and prove versions of these results over…
The second author formulated quantum unique ergodicity for Eisenstein series in the prime level aspect in "Equidistribution of Eisenstein series in the level aspect", Commun. Math. Phys. 289(3), 1131-1150 (2009). We point out errors and…
In the context of metric $f(R)$ gravity, the Geodesic Deviation Equation (GDE) was first studied in arXiv:1010.5279v3, giving a general expression and studying a particular case, the FLRW universe. In the paper arXiv:1312.2022v1 a similar…
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid finite element method (ATGFEM) of Li and…
For a finite point set $E\subset \mathbb{R}^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k + 1$ points in E such that the distance between a pair of points is specified if the…
We resolve a long-standing open problem posed by Federer concerning the rectifiability of the integral geometric measure with exponent p >1, thereby settling a question that has persisted since its formulation. While the main theorem is…
The purpose of this erratum is to correct the proof of Theorem A.0.1 in the appendix to our article ``Hadamard spaces with isolated flats'' math.GR/0411232, which was jointly authored by Mohamad Hindawi, Hruska and Kleiner. In that…
We give a self-contained, modern exposition of \'Edouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with $R$ a cubic or quartic polynomial that, despite living on a…
The paper is centered around a new proof of the infinitesimal rigidity of smooth closed surfaces with everywhere positive Gauss curvature. We use a reformulation that replaces deformation of an embedding by deformation of the metric inside…
An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.