Related papers: Correction to : The Kuo condition, an inequality o…
We correct the proof of Theorem 4.1 from [C. R. Math. Acad. Sci. Soc. R. Can. \textbf{44} (2022), no. 4, 88--112].
Sufficiency of jets is a very important notion introduced by Rene Thom in order to establish the structural stability theory. The criteria for some sufficiency of jets are known as the Kuo condition and Thom type inequality, which are…
We state and prove several characterizations of Thom's regularity condition for stratified maps. In particular we extend to stratified maps some characterizations of Whitney (a) regularity, due to the second author.
This version corrects a number of mistakes that appeared in the previous draft. In particular, the (EU-LREM) condition is sufficient for existence and uniqueness but not necessary, as we had claimed. We are grateful to P. C. B. Phillips and…
We show that the natural stratifications arising from certain deformation families of line singularities with constant L\^e numbers satisfy Bekka's $(c)$-regularity condition. As a corollary, we obtain that these families are topologically…
In this paper we prove a strong nonstructure theorem for kappa (T)-saturated models of a stable theory T with dop.
G{\"o}del's second incompleteness theorem forbids to prove, in a given theory U, the consistency of many theories-in particular, of the theory U itself-as well as it forbids to prove the normalization property for these theories, since this…
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
We discuss an extension of the $C$-theorem to chiral theories. We show that two monotonically decreasing $C$-functions can be introduced. However, their difference is a constant of the renormalization group flow. This constant reproduces…
Estimate (3.39) which appears in the proof of Proposition 3.4 in [Ann. Probab. 27 (1999) 1414--1467, doi:10.1214/aop/1022677454] is wrong. We present below a corrected proof which introduces an extra factor 2 in equations (3.34) and (3.35).…
There is a gap in the proof of Lemma VII.4 in [Ann. of Math. (2) 145 (1997), 81--137]. We present an alternative proof of Theorem B (C^1 Omega-stable vector fields satisfy Axiom A). The novel and essential part in the proof of the stability…
This paper continues the author's previous study \cite{Kura20}, showing that several weak principles inspired by non-normal modal logic suffice to derive various refined forms of the second incompleteness theorem. Among the main results of…
We adapt the method of Simon [JDG '93] to prove a $C^{1,\alpha}$-regularity theorem for minimal varifolds which resemble a cone $\bf{C}_0^2$ over an equiangular geodesic net. For varifold classes admitting a "no-hole" condition on the…
We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity…
When we investigate a type system, it is helpful if we can establish the well-foundedness of types or terms with respect to a certain hierarchy, and the Extended Calculus of Constructions (called $ECC$, defined and studied comprehensively…
In the article titled "Branching-Coalescing Particle Systems" published in Probability Theory and Related Fields 131(3), pages 376-414, (2005), Theorem 7 as stated there is incorrect. Indeed, we show by counterexample that the equality that…
We show that a suitable quantitative Fatou Theorem characterizes uniform rectifiability in the codimension 1 case.
We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…
We prove a c-theorem for holographic theories.
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.