Monge-Ampere foliations with singularities at the boundary of strongly convex domains

Let D subset of C-N be a bounded strongly convex domain with smooth boundary. We consider a Monge-Ampere type equation in D with a simple pole at the boundary. Using the Lempert foliation of D in extremal discs, we construct a solution u whose level sets are boundaries of horospheres. Among other things, we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution

The pluricomplex Poisson kernel for strongly convex domains

Let D be a bounded strongly convex domain in the complex space of dimension n. For a fixed point p epsilon partial derivative D, we consider the solution of a homogeneous complex Monge-Ampere equation with a simple pole at p. We prove that such a solution enjoys many properties of the classical Poisson kernel in the unit disc and thus deserves to be called the pluricomplex Poisson kernel of D with pole at p. In particular we discuss extremality properties (such as a generalization of the classical Phragmen-Lindelof theorem), relations with the pluricomplex Green function of D, uniqueness in terms of the associated foliation and boundary behaviors. Finally, using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions

Automorphisms of C-k with an invariant non-recurrent attracting Fatou component biholomorphic to C x (C*)(k-1)

We prove the existence of automorphisms of C-k , k >= 2, having an invariant, non-recurrent Fatou component biholomorphic to C x (C*)(k-1) which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component. As a corollary, we obtain a Runge copy of C x (C*)(k-1) in C-k. The constructed Fatou component also avoids k analytic discs intersecting transversally at the fixed point

Identity principles for commuting holomorphic self-maps of the unit disc

Some identity principles for holomorphic functions are investigated

Identity principles for commuting holomorphic self-maps of the unit disc

3Some identity principles for holomorphic functions are investigated.nonemixedF. BRACCI; R. TAURASO; VLACCI, FABIOF., Bracci; R., Tauraso; Vlacci, Fabi

Localization of Atiyah classes

We construct the Atiyah classes of holomorphic vector bundles using (1,0)-connections and developing a Chern–Weil type theory, allowing us to effectively compare Chern and Atiyah forms. Combining this point of view with the Čech–Dolbeault cohomology, we prove several results about vanishing and localization of Atiyah classes, and give some applications. In particular, we prove a Bott type vanishing theorem for (not necessarily involutive) holomorphic distributions. As an example we also present an explicit computation of the residue of a singular distribution on the normal bundle of an invariant submanifold that arises from the Camacho–Sad type localization

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Seismic Performance of Confined Sill Plate Connections

In the aftermath of the 1994 Northridge earthquake, extensive field investigations revealed damage in wood frame construction in the form of splitting of the 2 X 4 or 2 X 6 wood sill plates along the line of anchor bolts that typically connect shear walls to the masonry or concrete foundation. Due to the severity of such brittle failures, the city of Los Angeles has recently restricted the use of 2X dimension lumber in sill plates and requires the use of 3X dimension lumber. This paper presents an experimental investigation of the performance of 2X dimension lumber sill plate connections at the yield and ultimate limit states during incremental quasi-static reversed cyclic loading and suggests possible cost-effective retrofit strategies for their improved seismic performance without having to increase the sill plate thickness. Proposed retrofit strategies are based on providing confinement to the sill plate using metal reinforcing straps and reinforcing clamps to increase the deformation capability and energy dissipation capacity of the connection, while maintaining substantial levels of connection strengths

Fatou flowers and parabolic curves

In this survey we collect the main results known up to now (July 2015) regarding possible generalizations to several complex variables of the classical Leau-Fatou flower theorem about holomorphic parabolic dynamics