Related papers: A duality theorem for a four dimensional Willmore …
In this paper we leave the neighborhood of the singularity at the origin and turn to the singularity at the horizon. Using nonlinear superdistributional geometry and supergeneralized functions it seems possible to show that the horizon…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an…
We explore novel examples of RG flows preserving a non-invertible self-duality symmetry. Our main focus is on $\mathcal{N}=1$ quadratic superpotential deformations of 4d $\mathcal{N}=4$ super-Yang-Mills theory with gauge algebra…
We offer in this review a description of the vacuum energy of self-similar systems. We describe two views of setting self-similar structures and point out the main differences. A review of the authors' work on the subject is presented,…
There exists several modified gravity theories designed to reproduce the empirical Milgrom's formula (MOND). Here we derive analytical results in the context of the static weak-field limit of two of them (BIMOND, leading for a given set of…
Furthering the development of Da Lio-Gianocca-Rivi\`ere's Morse stability theory (arXiv:2212.03124) that was first applied to harmonic maps between manifolds and later extended to the case of Willmore immersions (arXiv:2306.04608-04609), we…
Recent Magnetospheric Multiscale (MMS) observations report approximate equality between electric and magnetic field energy spectral densities, $\varepsilon_{0} P[\delta E]/2 \approx P[\delta B]/(2\mu_{0})$, at sub-electron scales in…
Using the harmonic map heat flow, we construct an energy class for wave maps $\phi$ from two-dimensional Minkowski space $\R^{1+2}$ to hyperbolic spaces $\H^m$, and then show (conditionally on a large data well-posedness claim for such wave…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
In their proof of the positive energy theorem, Schoen and Yau showed that every asymptotically flat spacelike hypersurface M of a Lorentzian manifold which is flat along M can be isometrically imbedded with its given second fundamental form…
We study strong-weak coupling duality (S-duality) in N=4 supersymmetric non-Abelian Yang-Mills theories. These theories arise naturally as the low-energy limit of four-dimensional toroidal compactifications of the heterotic string. Firstly,…
We investigate on a Randall-Sundrum warped spacetime, a Kerr-like black hole in the conformal dilaton-Higgs $(\omega,\Phi)$ gravity model. We applied the antipodal boundary condition on the Klein surface using the $\mathds{Z}_2$-symmetry in…
In this work we present new fundamental tools for studying the variations of the Willmore functional of immersed surfaces into $R^m$. This approach gives for instance a new proof of the existence of a Willmore minimizing embedding of an…
For the class of approximate harmonic maps $u\in W^{1,2}(\Sigma,N)$ from a closed Riemmanian surface $(\Sigma,g)$ to a compact Riemannian manifold $(N, h)$, we show that (i) the so-called energy identity holds for weakly convergent…
It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. This…
We give sufficient and necessary geometric conditions, guaranteeing that an immersed compact closed manifold $\Sigma^m\subset \R^n$ of class $C^1$ and of arbitrary dimension and codimension (or, more generally, an Ahlfors-regular compact…
In this work, we derive an upper bound on energetic quantities, namely vacuum energy and free energy, for static solutions of Einstein-Scalar theory in four dimensional asymptotically locally Anti-de Sitter(AlAdS) spacetime with a…
The paper is devoted to the variational analysis of the Willmore, and other L^2 curvature functionals, among immersions of 2-dimensional surfaces into a compact riemannian m-manifold (M^m,h) with m>2. The goal of the paper is twofold, on…
Based on the observation that the dimension of the tangent space is not necessarily equal to the dimension of the corresponding curved manifold and on the known fact that gravitational theories can be formulated in a gauge theoretic way, we…
A triharmonic map is a critical point of the 3-energy in the space of smooth maps between two Riemannian manifolds. We study a triharmonic isometric immersion into a space form of non-positively constant curvature. We show that if the…