Related papers: A short proof of smooth implies flat
We show that a real rational (over $\C$) surfaces are quasi-simple, i.e., that such a surface is determined up to deformation in the class of real surfaces by the topological type of its real structure.
Flatness of sampled data systems can be characterized by a simple property. They must admit the transformation to special representations, which are the series or partial series connection of a Brunovsky normal form and a complement. It is…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…
We clarify the question whether for a smooth curve of polynomials one can choose the roots smoothly and related questions. Applications to perturbation theory of operators are given.
Mathematical proofs should be paired with formal proofs, whenever feasible.
Flatness measurement of a surface plate is an intensive and old research topic. However ISO definition related and other measurement methods seem uneasy in measuring and/ or complicated in data analysis. Especially in reality, the mentioned…
Principal affine open subsets in affine schemes are an important tool in the foundations of algebraic geometry. Given a commutative ring $R$, $\,R$-modules built from the rings of functions on principal affine open subschemes in…
We show that a compact complex surface which fibers smoothly over a curve of genus >1 with fibers of genus >1 fibers holomorphically. We deduce an improvement of a result in [D Kotschick, Math. Research Letters, 5 (1998) 227-234], and a…
It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.
We give an elementary short proof of Grothendieck's base change theorem for the cohomology of flat coherent sheaves.
A deflatable permutation class is one in which the simple permutations are contained in a proper subclass. Deflatable permutation classes are often easier to describe and enumerate than non-deflatable ones. Some theorems which guarantee…
Proving that a finitely generated convex cone is closed is often considered the most difficult part of geometric proofs of Farkas' lemma. We provide a short simple proof of this fact and (for completeness) derive Farkas' lemma from it using…
We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms.
We provide a short proof that an $L^2_1$ and $J$-holomorphic curve is in fact smooth. As an application, we deduce a removal of singularity theorem for curves of finite energy.
Polyhedral surfaces are fundamental objects in architectural geometry and industrial design. Whereas closeness of a given mesh to a smooth reference surface and its suitability for numerical simulations were already studied extensively, the…
We prove a formality theorem for algebraic objects internal to smooth complex varieties that are not compact but whose mixed Hodge structure has a certain purity property.
We prove that a complete, two-sided, stable minimal immersed hypersurface in $\mathbf{R}^{4}$ is flat.
Smooth hypoellipticity for scalar equations is quite well understood presently. On the other hand, much remains to be done for systems and/or at different levels of regularity and in particular for $L^1$-hypoellipticity. In this article we…
We show that every 'conveniently Hoelder' homomorphism between Lie groups in the sense of convenient differential calculus is smooth (in the convenient sense). In particular, every Lip^0 homomorphism is smooth.
We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.