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

Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher-order curvature corrections to General Relativity, still shares many of its features, such as second-order…

We prove positive mass theorem with angular momentum and charges for axially symmetric, simply connected, maximal, complete initial data sets with two ends, one designated asymptotically flat and the other either (Kaluza-Klein)…

We study development of singularities for the spherically symmetric Yang-Mills equations in $d+1$ dimensional Minkowski spacetime for $d=4$ (the critical dimension) and $d=5$ (the lowest supercritical dimension). Using combined numerical…

We prove that compact Calabi--Yau varieties with certain isolated singularities are projective. In dimension 3 we do this by analysis, supposing given conifold metrics. In higher dimensions it follows more readily from Ohsawa's degenerate…

A mechanism for determining fermion masses in four spacetime dimensions is presented, which uses a scalar-field domain wall extending in a fifth spacelike dimension and a special choice of Yukawa coupling constants. A bounded and discrete…

Yang Mills theory in 2+1 dimensions can be expressed as an array of coupled (1+1)-dimensional principal chiral sigma models. The $SU(N)\times SU(N)$ principal chiral sigma model in 1+1 dimensions is integrable, asymptotically free and has…

For an asymptotically flat initial data, the Penrose inequality gives a lower bound of the Arnowitt-Deser-Misner total mass of a spacetime in terms of the area of certain surfaces representing black holes. This is a deep and beautiful…

First we argue in an informal, qualitative way that it is natural to enlarge space-time to five dimensions to be able to solve the problem of elementary particle masses. Several criteria are developed for the success of this program.…

Building upon dimension reduction techniques in the study of positive scalar curvature (PSC) geometry, we prove an effective version of the positive mass theorem (PMT) for asymptotically flat (AF) manifolds of dimension $n\leq 8$ with…

We revisit the problem of solving the Einstein constraint equations in vacuum by a new method, which allows us to prescribe four scalar quantities, representing the full dynamical degrees of freedom of the constraint system. We show that…

We consider generic 2 x 2 singular Liouville systems on a smooth bounded domain in the plane having some symmetry with respect to the origin. We construct a family of solutions to which blow-up at the origin and whose local mass at the…

We extend the notion of the Nieh-Yan invariant to generic metric-affine geometries, where both torsion and nonmetricity are taken into account. Notably, we show that the properties of projective invariance and topologicity can be…

The attractor mechanism in five dimensional Einstein-Maxwell Chern-Simons theory is studied. The expression of the five dimensional rotating black object potential depending on Taub-NUT, electric and magnetic charges as well as on all the…

A method of calculating Feynman diagrams from their small momentum expansion [1] is extended to diagrams with zero mass thresholds. We start from the asymptotic expansion in large masses [2] (applied to the case when all $M_i^2$ are large…

Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of…

We provide optimal pinching results on closed Einstein manifolds with positive Yamabe invariant in any dimension, extending the optimal bound for the scalar curvature due to Gursky and LeBrun in dimension four. We also improve the known…

A recently formulated conjecture of Gamayun, Iorgov and Lisovyy gives an asymptotic expansion of the Jimbo--Miwa--Ueno isomonodromic $\tau$-function for certain Painlev\'e transcendents. The coefficients in this expansion are given in terms…

We perform dimensional reductions of recently constructed self-dual $~N=2$~ {\it supersymmetric} Yang-Mills theory in $~2+2\-$dimensions into two-dimensions. We show that the universal equations obtained in these dimensional reductions can…

In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…

We prove the positive mass theorem for asymptotical flat (AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead we use the conformal blow up technique which dates back to…