Related papers: Smooth hyperbolicity cones are second-order cone r…

We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supported sections are dense in the domains of these operators.…

Representation theorems relate seemingly complex objects to concrete, more tractable ones. In this paper, we take advantage of the abstraction power of category theory and provide a general representation theorem for a wide class of…

The Serre conjecture II predicts that every torsor under a semisimple, simply connected, algebraic group over a field of cohomological dimension at most 2 and of degree of imperfection at most 1 has a rational point. We generalize this…

If $X$ is an $n\times n$ symmetric matrix, then the directional derivative of $X \mapsto \det(X)$ in the direction $I$ is the elementary symmetric polynomial of degree $n-1$ in the eigenvalues of $X$. This is a polynomial in the entries of…

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have…

Kato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely…

We study basic properties of the category of smooth representations of a p-adic group G with coefficients in any commutative ring R in which p is invertible. Our main purpose is to prove that Hecke algebras are noetherian whenever R is ; a…

We prove the Bloch conjecture : $ c_2(E) \in H^4_\cald (X,\bbz(2))$ is torsion for holomorphic rank two vector bundles $E$ with an integrable connection over a complex projective variety $X$. We prove also the rationality of the…

Firstly we show a generalization of the (1,1)-Lefschetz theorem for projective toric orbifolds and secondly we prove that on 2k-dimensional quasi-smooth hypersurfaces coming from quasi-smooth intersection surfaces, under the Cayley trick,…

We show that the strongly symmetric spectral convex compact sets are precisely the normalized state spaces of finite-dimensional simple Euclidean Jordan algebras and the simplices. Spectrality is the property that every state has a convex…

In this paper, the geometry properties of Hankel form are studied, including their positive semi-definite (PSD) cone and sum-of-squares (SOS) cone. We denote them by $HPSD(m,n)$ and $HSOS(m,n)$, respectively. We show that both $HPSD(m,n)$…

We study the different notions of semipositivity for (1,1) cohomology classes on K3 surfaces. We first show that every big and nef class (and every nef and rational class) is semiample, and in particular it contains a smooth semipositive…

In this paper, we give a sufficient condition to guarantee the existence of a smooth solution of the Navier-Stokes Equation with the nice decreasing properties at infinity. In this way, we prove the existence of smooth physically reasonable…

The second-order cone plays an important role in convex optimization and has strong expressive abilities despite its apparent simplicity. Second-order cone formulations can also be solved more efficiently than semidefinite programming in…

The celebrated Nash Embedding Theorem asserts that every closed Riemannian manifold can be isometrically embedded into a sufficiently high-dimensional Euclidean space. In this paper, we prove an analogous result in the conformally compact…

Let G be a connected reductive algebraic group over an algebraically closed field k. In a recent paper, Bate, Martin, R\"ohrle and Tange show that every (smooth) subgroup of G is separable provided that the characteristic of k is very good…

It is shown that a smooth bounded pseudoconvex complete Hartogs domain in $\mathbb{C}^2$ has trivial Nebenh\"ulle. The smoothness assumption is used to invoke a theorem of D. Catlin.

We introduce the notions of symmetric and symmetrizable representations of $\text{SL}_2(\mathbb{Z})$. The linear representations of $\text{SL}_2(\mathbb{Z})$ arising from modular tensor categories are symmetric and have congruence kernel.…

We prove that every locally conformally flat metric on a closed, oriented hyperbolic 4-manifold with scalar curvature bounded below by -12 satisfies Schoen's conjecture. We also classify all closed Riemannian 4-manifolds of positive scalar…

Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper, we show that, conversely, axially symmetric closed genus…