Related papers: Dihedral rigidity for cubic initial data sets
In this paper we consider 2+1-dimensional gravity coupled to N point-particles. We introduce a gauge in which the $z$- and $\bar{z}$-components of the dreibein field become holomorphic and anti-holomorphic respectively. As a result we can…
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This…
We prove that any properly oriented $C^{2,1}$ isometric immersion of a positively curved Riemannian surface M into Euclidean 3-space is uniquely determined, up to a rigid motion, by its values on any curve segment in M. A generalization of…
A rigidity property for the homotopy invariant stable linear framed presheaves is established. As a consequence a variant of Gabber rigidity theorem is obtained for a cohomology theory representable in the motivic stable homotopy category…
We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors. We further point out which constrained…
In the thesis, results presented in various papers involving the author are reviewed. First, general results about consistent deformations at first order (i.e. cubic) using the antifield formalism in Minkowski spacetime are gathered.…
In [M3], Milnor found Tricorn-like sets in the parameter space of real cubic polynomials. We give a rigorous definition of these Tricorn-like sets as suitable renormalization loci, and show that the dynamically natural straightening map…
We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…
We prove the Poisson version of the Gromov-Eliashberg's $C^0$-rigidity. More precisely, we prove that the group of Poisson diffeomorphisms is closed with respect to the $C^0$ topology inside the group of all diffeomorphisms. The proof…
Uniqueness (up to isometries) and existence of limits are studied in the context of Cheeger-Gromov convergence of spacetimes. To address the non-compactness of the vector isometry group in the semi-Riemannian setting, standard pointed…
We prove the K-moduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K-(semi,poly)-stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In…
We study a deSitter/Anti-deSitter/Poincare Yang-Mills theory of gravity in d-space-time dimensions in an attempt to retain the best features of both general relativity and Yang-Mills theory: quadratic curvature, dimensionless coupling and…
Let M be a closed minimal hypersurface in 5-dimensional Euclidean sphere with constant nonnegative scalar curvature. We prove that, if the sum of the cubes of all principal curvatures and the number of distinct principal curvatures are…
In this paper we propose two guiding principles that suggest a number of conjectures (some now proved) about various forms of rigidity for moduli spaces arising in algebraic geometry. Such conjectures have group-theoretic, topological and…
We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question of Gromov (1993) and is in contrast to the fact that any metric space embeds coarsely into an Alexandrov space…
For any intrinsic Gromov hyperbolic space we establish a Gehring-Hayman type theorem for conformally deformed spaces. As an application, we prove that any complete intrinsic hyperbolic space with atleast two points in the Gromov boundary…
This article represents the first installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on sharp cubic energy estimates. Precisely, we introduce and…
Let $G:\mathbb{R\rightarrow R}$ be a continuous function. In the first part of this paper, we investigate sufficient conditions on $G$ such that \begin{equation*} \{G(f):f\in \dot{K}_{p,q}^{\alpha }F_{\beta }^{s}\}\subset…
We prove Llarull-type rigidity for $S^{n-m}\times\mathbb{T}^m$ ($3\le n\le 7$, $1\le m\le n-2$). If a closed spin $(M^n,g)$ admits a degree-nonzero map to $S^{n-m}\times\mathbb{T}^m$ whose spherical projection is area non-increasing, and…
The famous example of the double-Watt mechanism given by Connelly and Servatius raises some problems concerning the classical definitions of higher-order flexibility and rigidity, respectively, as they attest the cusp configuration of the…