Related papers: Smoothing theory revisited

We present in this work a new and simple proof of the false centre theorem.

We prove a Wong-Rosay type theorem for a domain with a piecewise smooth generic strictly pseudoconvex boundary point.

We improve the main results in the paper from the title using a recent refinement of Bronshtein's theorem due to Colombini, Orr\'u, and Pernazza. They are then in general best possible both in the hypothesis and in the outcome. As a…

We give a new proof of a theorem by M.P. do Carmo and M. Dajczer on helicoidal surfaces of constant mean curvature.

We prove a vanishing theorem for the twisted de Rham cohomology of a compact manifold.

We prove the subsolution theorem for the complex Hessian equations in a smoothly bounded strongly $m$-pseudoconvex domain, $1 < m < n$, in $\bC^n$.

In this revised form, the proof of the principal lemma has been simplified and the main theorem has been extended to all characteristics for those varieties which are smooth in codimension one. This principal theorem essentially says the…

In this paper, we prove existence of smooth solutions of the Navier-Stokes equations that gives a positive answer to the problem proposed by Fefferman [3].

We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…

We provide new sufficient conditions under which Ryser's conjecture holds.

We prove the two theorems of the title, settling two long standing questions in the local theory of singular minimal hypersurfaces. The sharpness of either result is with respect to its hypothesis on the size of the allowable singular sets.…

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.

In Theorem 3.1 of [12], we proved a rigidity result for self-shrinkers under the integral condition on the norm of the second fundamental form. In this paper, we relax the such bound to any finite constant (see Theorem 4.4 for details).

In this paper we state and prove ad hoc "Separation Theorems" of the so-called Smooth Commutative Algebra, the Commutative Algebra of \(\mathcal{C}^{\infty}-\)rings. These results are formally similar to the ones we find in (ordinary)…

We provide an axiomatic framework for the study of smooth extensions of generalized cohomology theories. Our main results are about the uniqeness of smooth extensions, and the identification of the flat theory with the R/Z-theory. In…

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We give a short proof of Wolff-Denjoy theorem for (not necessarily smooth) strictly convex domains. With similar techniques we are also able to prove a Wolff-Denjoy theorem for weakly convex domains, again without any smoothness assumption…

The classical Theorem of Mumford states that a topologically regular complex algebraic surface in $\mathbb{C}^3$ with an isolated singular point is smooth. We proof that any Lipschitz regular complex algebraic set is smooth. No restriction…