Novel schedule for treatment of inflammatory breast cancer

Inflammatory breast cancer (IBC) is the most aggressive form of this tumor, with the clinical and biological characteristics of a rapidly proliferating disease. This tumor is always diagnosed at advanced stages, atleast stage IIIB (locally advanced), so its management requires an integrated multidisciplinary approach with a systemic therapy followed by surgery and radiation therapy. Patients with IBC usually have a worse prognosis but the achievement of a pathologic complete response after neoadjuvant chemotherapy may have good rates of overall survival. We present the case of a 47 year old women with IBC, luminal B and with high proliferative index; she was successfully treated with a sequential schedule of chemotherapy (anthracyclines dose-dense/carboplatin+ taxane/Cyclophosphamide Methotrexate Fluorouracil), hormone-therapy, complementary radiotherapy and finally surgery until the achievement of a complete clinical and pathological response. Luminal B inflammatory breast cancer with high proliferation index can benefit from sequential schedules of neoadjuvant chemotherapy and hormonal treatment and this can result in pathological complete response

A Remark on Boundary Effects in Static Vacuum Initial Data sets

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that the boundary of (M, g) has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that the boundary has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the area and mean curvature of the boundary. Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit

Specifying angular momentum and center of mass for vacuum initial data sets

We show that it is possible to perturb arbitrary vacuum asymptotically flat spacetimes to new ones having exactly the same energy and linear momentum, but with center of mass and angular momentum equal to any preassigned values measured with respect to a fixed affine frame at infinity. This is in contrast to the axisymmetric situation where a bound on the angular momentum by the mass has been shown to hold for black hole solutions. Our construction involves changing the solution at the linear level in a shell near infinity, and perturbing to impose the vacuum constraint equations. The procedure involves the perturbation correction of an approximate solution which is given explicitly.Comment: (v2) a minor change in the introduction and a remark added after Theorem 2.1; (v3) final version, appeared in Comm. Math. Phy

Gluing construction of initial data with Kerr-de Sitter ends

We construct initial data sets which satisfy the vacuum constraint equa- tions of General Relativity with positive cosmologigal constant. More pre- silely, we deform initial data with ends asymptotic to Schwarzschild-de Sitter to obtain non-trivial initial data with exactly Kerr-de Sitter ends. The method is inspired from Corvino's gluing method. We obtain here a extension of a previous result for the time-symmetric case by Chru\'sciel and Pollack.Comment: 27 pages, 3 figure

A new geometric invariant on initial data for Einstein equations

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the non-time symmetric cas

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.Comment: This third and final version has been accepted for publication in Communications in Mathematical Physic

CYK Tensors, Maxwell Field and Conserved Quantities for Spin-2 Field

Starting from an important application of Conformal Yano--Killing tensors for the existence of global charges in gravity, some new observations at \scri^+ are given. They allow to define asymptotic charges (at future null infinity) in terms of the Weyl tensor together with their fluxes through \scri^+. It occurs that some of them play a role of obstructions for the existence of angular momentum. Moreover, new relations between solutions of the Maxwell equations and the spin-2 field are given. They are used in the construction of new conserved quantities which are quadratic in terms of the Weyl tensor. The obtained formulae are similar to the functionals obtained from the Bel--Robinson tensor.Comment: 20 pages, LaTe

Conformal scattering for a nonlinear wave equation on a curved background

The purpose of this paper is to establish a geometric scattering result for a conformally invariant nonlinear wave equation on an asymptotically simple spacetime. The scattering operator is obtained via trace operators at null infinities. The proof is achieved in three steps. A priori linear estimates are obtained via an adaptation of the Morawetz vector field in the Schwarzschild spacetime and a method used by H\"ormander for the Goursat problem. A well-posedness result for the characteristic Cauchy problem on a light cone at infinity is then obtained. This requires a control of the nonlinearity uniform in time which comes from an estimates of the Sobolev constant and a decay assumption on the nonlinearity of the equation. Finally, the trace operators on conformal infinities are built and used to define the conformal scattering operator

Gluing Initial Data Sets for General Relativity

We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Secondly, the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place. Using this construction we establish the existence of cosmological, maximal globally hyperbolic, vacuum space-times with no constant mean curvature spacelike Cauchy surfaces.Comment: Final published version - PRL, 4 page

On the volume functional of compact manifolds with boundary with constant scalar curvature

We study the volume functional on the space of constant scalar curvature metrics with a prescribed boundary metric. We derive a sufficient and necessary condition for a metric to be a critical point, and show that the only domains in space forms, on which the standard metrics are critical points, are geodesic balls. In the zero scalar curvature case, assuming the boundary can be isometrically embedded in the Euclidean space as a compact strictly convex hypersurface, we show that the volume of a critical point is always no less than the Euclidean volume bounded by the isometric embedding of the boundary, and the two volumes are equal if and only if the critical point is isometric to a standard Euclidean ball. We also derive a second variation formula and apply it to show that, on Euclidean balls and ''small'' hyperbolic and spherical balls in dimensions 3 to 5, the standard space form metrics are indeed saddle points for the volume functional