Related papers: Rigidity of Kac-Schwarz operators

The explicit description of irreducible homogeneous operators in the Cowen-Douglas class and the localization of Hilbert modules naturally leads to the definition of a smaller class of Cowen-Douglas operators possessing a flag structure.…

We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^c case. In particular, we prove a K-theory version of the main results of [{\bf H}], [{\bf Liu1}, Theorem B] for a family of almost complex manifolds.

The formal rigidity of the Witt and Virasoro algebras was first established by the author in [4]. The proof was based on some earlier results of the author and Goncharowa, and was not presented there. In this paper we give an elementary…

In this paper, we give the rigidity theorem for a log morphism as an extension of a fixed scheme morphism. We also give several applications of the rigidity theorem.

Consider a linear space L of complex D-dimensional linear operators, and assume that some power L^k of L is the whole space of DxD matrices. Perez-Garcia, Verstraete, Wolf and Cirac conjectured that the sequence L^1,L^2,... stablilizes…

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality…

We review the construction of generalized integrable hierarchies of partial differential equations, associated to affine Kac-Moody algebras, that include those considered by Drinfel'd and Sokolov. These hierarchies can be used to construct…

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy--Littlewood--Sobolev theorem in this context. In our main result, we investigate the dependence of…

Using the index theory for twisted Dirac operators acting on sections of Lipschitz bundles over non-compact manifolds, we prove Llarull-type comparison results in scalar curvature geometry. They apply to spin Riemannian manifolds with…

First the Hardy and Rellich inequalities are defined for the submarkovian operator associated with a local Dirichlet form. Secondly, two general conditions are derived which are sufficient to deduce the Rellich inequality from the Hardy…

In 1983 A. Suslin proved the Quillen-Lichtenbaum conjecture about algebraic K-theory of algebraically closed fields. The proof was based on a theorem called the Suslin rigidity theorem. In the present paper we prove the rigidity theorem for…

We find explicit stability bounds for exponential Riesz bases on domains of R^d. Our results generalize Kadec theorem and other stability theorems in the literature.

We prove a Jebsen-Birkhoff like theorem for f(R) theories of gravity in order to to find the necessary conditions required for the existence of the Schwarzschild solution in these theories and demonstrate that the rigidity of such solutions…

For any finite group G, we show that the 2-local G-equivariant stable homotopy category, indexed on a complete G-universe, has a unique equivariant model in the sense of Quillen model categories. This means that the suspension functor,…

We show rigidity results for the operator equations T(f.g) = Tf.Tg, T(f*g) = Tf.Tg and T(f.g) = Tf*Tg for bijective operators T acting on sufficently large spaces of smooth functions. Typically a condition like |T(f.g) - Tf.Tg| < a for all…

In this paper, we prove a sharp, weighted Hardy-type inequality for the Dirac operator. A key feature of our result is that the inequality is not only sharp but also attained, and we construct explicit minimizers that satisfy the equality…

Recently, Darmon and Vonk initiated the theory of rigid meromorphic cocycles for the group $\mathrm{SL}_2(\mathbb{Z}[1/p])$. One of their major results is the algebraicity of the divisor associated to such a cocycle. We generalize the…

In this paper we introduce the notion of rigidity for harmonic-Ricci solitons and we provide some characterizations of rigidity, generalizing some known results for Ricci solitons. In the compact case we are able to deal with not…

We establish long-time stability of multi-dimensional viscous shocks of a general class of symmetric hyperbolic--parabolic systems with variable multiplicities, notably including the equations of compressible magnetohydrodynamics (MHD) in…

A version of Arzel\`a-Ascoli theorem for $X$ being $\sigma$-locally compact Hausdorff space is proved. The result is used in proving compactness of Fredholm, Hammerstein and Urysohn operators. Two fixed point theorems, for Hammerstein and…