Related papers: A dimension descent scheme for the positive mass t…

We solve a generalization of ordinary N=1 super Yang-Mills theory with gauge group U(N) and an adjoint chiral multiplet X for which we turn on both an arbitrary tree-level superpotential term \int d^{2}\theta Tr W(X) and an arbitrary…

We give an alternative proof of the Schoen--Simon--Yau curvature estimates and associated Bernstein-type theorems (1975), and extend the original result by including the case of $6$-dimensional (stable minimal) immersions. The key step is…

It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for…

We prove a positive energy theorem in 2+1 dimensional gravity for open universes and any matter energy-momentum tensor satisfying the dominant energy condition. We consider on the space-like initial value surface a family of widening Wilson…

J. Rosenberg's $\mathbb{S}^1$-stability conjecture states that a closed oriented manifold $X$ admits a positive scalar curvature metric iff $X\times \mathbb{S}^1$ admits a positive scalar curvature metric $h$. As pointed out by J. Rosenberg…

We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider…

We explore new symmetries in two-component third-order Burgers' type systems in (1+1)-dimension using Wang's O-scheme. We also find a master symmetry for a (2+1)-dimensional Davey-Stewartson type system. These results shed light on the…

This paper explores the conditions under which modified gravitational theories admit the positive mass. Following Witten's spinor argument, it is argued that a single condition should be imposed upon a gauge connection in the…

This paper develops a theory of symplectic reduction in the infinite-dimensional setting, covering both the regular and singular case. Extending the classical work of Marsden, Weinstein, Sjamaar and Lerman, we address challenges unique to…

We revisit the smallest non-physical singularity of the hard-sphere model in one dimension, also known as Tonks gas. We give an explicit expression of the free energy and reduced correlations at negative real fugacity and elaborate the…

Gauge theories induced by scalars in the fundamental representation of the $U(N_c)_{gauge}\times U(N_f)_{global}$ group are investigated in the large $N_c$ and $N_f$ limit. A master field is defined from bilinears of the scalar field…

The well-known Yang-Mills theory with one $ S^{1} / Z_{2}$ universal extra dimension (UED) is generalized to an arbitrary number of spatial extra dimensions through a novel compactification scheme. In this paper, the Riemannian flat based…

We propose a program for establishing a conjectural extension to the class of (origin-symmetric) log-concave probability measures $\mu$, of the classical dual Sudakov Minoration on the expectation of the supremum of a Gaussian process:…

We construct non-compactness examples for the fully coupled Einstein-Lichnerowicz constraint system in the focusing case. The construction is obtained by combining pointwise a priori asymptotic analysis techniques, finite-dimensional…

We prove a positive mass theorem for continuous Riemannian metrics in the Sobolev space $W^{2, n/2}_{\mathrm{loc}}(M)$. We argue that this is the largest class of metrics with scalar curvature a positive a.c. measure for which the positive…

We use planar coordinates as well as hyperbolic coordinates to separate the de Sitter spacetime into two parts. These two ways of cutting the de Sitter give rise to two different spatial infinities. For spacetimes which are asymptotic to…

It is proven that the physical measure for the two-dimensional Yang-Mills theory is purely singular with respect to the kinematical Ashtekar-Lewandowski measure. For this, an explicit decomposition of the gauge orbit space into supports of…

For the first time, a complete classification of all constant solutions of the Yang-Mills-Dirac equations with SU(2) gauge symmetry in Minkowski space ${\mathbb R}^{1,3}$ is given. The explicit form of all solutions is presented. We use the…

We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $\mathbb{Z}_2$-group, using for the first time a min-max scheme in the singular setting. In our variational argument we need to deform…

We study regular, static, spherically symmetric solutions of Yang-Mills theories employing higher order invariants of the field strength coupled to gravity in $d$ dimensions. We consider models with only two such invariants characterised by…