相关论文: A uniform estimate for general quaternionic Calabi…
We use equivariant methods to establish basic properties of orbifold K-theory. We introduce the notion of twisted orbifold K-theory in the presence of discrete torsion, and show how it can be explicitly computed for global quotients.
We examine the numerical approximation of time-dependent Hamilton-Jacobi equations on networks, providing a convergence error estimate for the semi-Lagrangian scheme introduced in (Carlini and Siconolfi, 2023), where convergence was proven…
The wardian solution of any $\psi$-difference linear nonhomogeneous equation is found in the framework of the generalized finite operator calculus . Specifications to $q$-calculus case and the new one fibonomial calculus case are made…
The Hamilton-Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.
In this paper, we establish universal inequalities for eigenvalues of the clamped plate problem on compact submanifolds of Euclidean spaces, of spheres and of real, complex and quaternionic projective spaces. We also prove similar results…
Following the Cartans's original method of equivalence supported by methods of parabolic geometry, we provide a complete solution for the equivalence problem of quaternionic contact structures, that is, the problem of finding a complete…
This paper is devoted to proving the almost global solvability of the Cauchy problem for the Kirchhoff equation in the Gevrey space $\gamma^s_{\eta,L^2}$. Furthermore, similar results are obtained for the initial-boundary value problems in…
We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex…
We establish a priori Lipschitz estimates for unbounded solutions of second-order Hamilton-Jacobi equations in R^N in presence of an Ornstein-Uhlenbeck drift. We generalize the results obtained by Fujita, Ishii \& Loreti (2006) in several…
We prove that the categorical entropy of the autoequivalence $T_{\mathcal{O}}\circ(-\otimes\mathcal{O}(-1))$ on a Calabi-Yau manifold is the unique positive real number $\lambda$ satisfying $$ \sum_{k\geq…
A manifold (M,I,J,K) is called hypercomplex if I,J,K are complex structures satisfying quaternionic relations. A quaternionic Hermitian metric is called HKT (hyperkaehler with torsion) if $Id\omega_I = Jd \omega_J=Kd\omega_K$, where…
We put into light some generalized almost quaternionic and almost para-quaternionic structures and characterize their integrability with respect to a $\nabla$-bracket on the generalized tangent bundle $TM\oplus T^*M$ of a smooth manifold…
We extend the previous computations of Hermitian Yang-Mills connections for bundles on complete intersection Calabi-Yau manifolds to bundles on their free quotients. Bundles on quotient manifolds are often defined by equivariant bundles on…
It is well known that uniform resolvent estimates imply spectral cluster estimates. We show that the converse is also true in some cases. In particular, the universal spectral cluster estimates of Sogge \cite{MR930395} for the…
We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and…
This paper develops and analyzes a generic method for reconstructing solutions to the abstract Cauchy problem in a general Hilbert space, from noisy measured data. The method is based on the relationship between a partial differential…
We develop an operator algebraic framework for generalized Cardano polynomials and show how their structure naturally leads to an operator formulation of Cardano method that is compatible with tools and concepts from quantum information…
We prove that a contractible orbifold is a manifold.
It is well-known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz continuous when the Lagrangian depends on t. Similarly, for viscosity solutions to time-dependent Hamilton-Jacobi equations one…
This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an…