Related papers: The Bartnik quasi-local mass conjectures

In this paper, we investigate containment statements between symbolic and ordinary powers and bounds on the Waldschmidt constant of defining ideals of points in projective spaces. We establish the stable Harbourne conjecture for the…

This article considers the quasi-local energy in reference to a general static spacetime. We follow the approach developed by the authors in [19, 20, 7, 9] and define the quasi-local energy as a difference of surface Hamiltonians, which are…

Verlinde conjectured eight years ago that gravitation might be an emergent entropic force. This rather surprising assertion was proved in [Physica A {\bf 505} (2018) 190] within a purely classical statistical context, and in [DOI:…

Mach's principle applied to rotation can be correct if one takes into account the rotation of the quantum vacuum together with the Universe. Whether one can detect the rotation of the vacuum or not depends on its properties. If the vacuum…

Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwisely weakly weighted (generalised) quasi-metrics. We then systematise and extend…

We study some particular cases of Viterbo's conjecture relating volumes of convex bodies and actions of closed characteristics on their boundaries, focusing on the case of a Hamiltonian of classical mechanical type, splitting into summands…

Shape theory works nice for (Hausdorff) paracompact spaces, but for spaces with no separation axioms, it seems to be quite poor. However, for finite and locally finite spaces their weak homotopy type is rather rich, and is equivalent to the…

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals, however this does not satisfy the obvious form of the Schr\"odinger equation. For…

The article provides a counterexample to a conjecture by Blocki-Zwonek.

Whether energy is conserved in a universe which keeps expanding is an intriguing question. It is tempting to argue that the total energy within the universe would have to increase as the universe expands. Upon more detailed inspection the…

This paper presents an approach to the creation of a variant of Extended Special Relativity that takes into consideration the existence of limiting relativistically invariant quantities (Planck parameters). It shows the possibility of…

We discuss the relation between the concentration of the Brown-York mass and the formation of trapped surfaces in non-spherical massive systems. In particular, we formulate and prove a precise version of the Thorne hoop conjecture in…

Relativistic length contraction is revisited and a simple but new thought experiment is proposed in which an apparent asymmetric situation is developed between two different inertial frames regarding detection of light that comes from a…

The idea that the vacuum energy density $\rho_{\Lambda}$ could be time dependent is a most reasonable one in the expanding Universe; in fact, much more reasonable than just a rigid cosmological constant for the entire cosmic history. Being…

It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary…

The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic…

Despite the many efforts, our theoretical understanding of the ultimate nature of the dark energy component of the universe still lags well behind the astounding experimental evidence achieved from the increasingly sophisticated…

We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.

In this paper, we introduce the concepts of m-quasiconvex, originally m-quasiconvex,and generalized m-quasiconvex functionals on topological vector spaces. Then we extend the concept of point separable topological vector spaces (by the…

The problem of quantum gravity is treated from a radically new viewpoint based on a detailed mathematical analysis of what the constitution of physical space is, which has been carried out by Michel Bounias and the author. The approach…