This paper is an overview of aspects of the singularities of the zeta function, equivalently, of the small time asymptotics of the trace of the heat semigroup, of elliptic cone operators. It begins with a brief description of classical results for regular differential operators on smooth manifolds, and includes a concise introduction to the theory of cone differential operators. The later secti...

Let ⇢ Rn be a bounded open set satisfying the uniform exterior cone condition. Let A be a uniformly elliptic operator given by

The pseudorapidity dependence of elliptic flow in Au+Au collisions at 130 A GeV is studied within a full three-dimensional hydrodynamic model in the light-cone coordinate. First, we prepare two initial conditions in the hydrodynamic model for analyzing elliptic flow. Both initial conditions lead to reasonable agreement with single particle spectra in central and semi-central collisions. Next, b...

In considering a class of quasilinear elliptic equations on a Riemannian manifold with nonnegative Ricci curvature, we give a new proof of Tolksdorf’s result on the construction of separable p-harmonic functions in a cone. 1991 Mathematics Subject Classification. 35K60 .

Abstract. Second-order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state. In contrast to former publications on this subject, the cone of critical directions is the smallest possible in the sense that the second-order sufficient conditions are the closest to the associat...

We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. For nondivergence elliptic equations in domains satisfying an exterior cone condition, similar results were obtained by J. H. Michael, who in turn relied on the barrier techniques due to K. Miller. Our approach is based on...

We study positive supersolutions to an elliptic equation (∗) −∆u = c|x|u, p, s ∈ R, in cone–like domains in R (N ≥ 2). We prove that in the sublinear case p < 1 there exists a critical exponent p∗ < 1 such that equation (∗) has a positive supersolution if and only if −∞ < p < p∗. The value of p∗ is determined explicitly by s and the geometry of the cone.

We investigate int-amplified endomorphisms on normal projective surfaces. prove that the output of equivariant MMP is either a Q-abelian surface, (equivariant) quasi-étale quotient smooth Mori dream space, or cone an elliptic curve.

Given a cone pseudodifferential operator P we give a full asymptotic expansion as t → 0 of the trace TrPe, where A is an elliptic cone differential operator for which the resolvent exists on a suitable region of the complex plane. Our expansion contains log t and new (log t) terms whose coefficients are given explicitly by means of residue traces. Cone operators are contained in some natural al...