Related papers: Convex Integration Theory without Integration

We show that certain vertex algebras without vacuum vector may be embedded into vertex algebras. The result is a partial analogue of the simple classical fact that any rng can be embedded into a ring. A one-line proof of the case of a…

In this paper, we study the smooth isometric immersion of a complete, simply connected surface with a negative Gauss curvature into the three-dimensional Euclidean space. A fundamental and longstanding problem is to find a sufficient…

Using convex integration we give a constructive proof of the well-known fact that every continuous curve in a contact $3$-manifold can be approximated by a Legendrian curve.

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a new developed…

Given any short immersion from an $n$-dimensional bounded and simply connected domain into $\mathbb{R}^{n+1}$ and any H\"older exponent $\alpha<(1+n^2-n)^{-1}$, we construct a $C^{1, \alpha}$ isometric immersion arbitrarily close in the…

We prove via convex integration a result that allows to pass from a so-called subsolution of the isentropic Euler equations (in space dimension at least $2$) to exact weak solutions. The method is closely related to the incompressible…

A version of Connes Integration Formula which provides concrete asymptotics of the eigenvalues is given. This radically extending the class of quantum-integrable functions on compact Riemannian manifolds.

Integral relations with the Cauchy kernel on a semi-axis for the Laguerre polynomials, the confluent hypergeometric function, and the cylindrical functions are derived. A part of these formulas is obtained by exploiting some properties of…

A proof of the isometric embedding of a given two-metric in E^3 of class C^1. The method uses the theory of first order partial differential equations. The curvature of the metric plays no role in the proof.

Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonlinear eigenvalue problems. We present a natural generalization…

We propose to take a look at a new approach to the study of integral polyhedra. The main idea is to give an integral representation, or matrix model representation, for the key combinatorial characteristics of integral polytopes. Based on…

Singular complex analytic vector fields on the Riemann surfaces enjoy several geometric properties (singular means that poles and essential singularities are admissible). We describe relations between singular complex analytic vector fields…

Let $G$ be a real Lie group with Lie algebra $\mathfrak g$. Given a unitary representation $\pi$ of $G$, one obtains by differentiation a representation $d\pi$ of $\mathfrak g$ by unbounded, skew-adjoint operators. Representations of…

We introduce a new convexified matching method for missing value imputation and individualized inference inspired by computational optimal transport. Our method integrates favorable features from mainstream imputation approaches: optimal…

We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the Gamma-class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for…

This is the third of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie, made parallel to the given R direction) by an…

We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer…

We give a new characterisation of the unparametrised geodesics, or distinguished curves, for affine, pseudo-Riemannian, conformal, and projective geometry. This is a type of moving incidence relation. The characterisation is used to provide…

We present a method for constructing harmonic immersions in $\mathbb{R}^3$, known as the Enneper-type representation. We also prove that any harmonic immersion in $\mathbb{R}^3$ can be obtained using this approach. Furthermore, we determine…

The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle…