Related papers: Routh's Theorem for Tetrahedra
In this paper we show an index theorem for gerbes
The theorem of Mather on generic projections of smooth algebraic varieties is also proved for the singular ones.
The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by…
In this note, simple proofs of certain well-known results involving the positive square root of positive matrices are given.
We give a new proof for the directional billiard complexity in the cube, which was conjectured in \cite{Ra} and proven in \cite{Ar.Ma.Sh.Ta}. Our technique gives us a similar theorem for some rational polyhedra.
We prove the Nagell-Lutz theorem for the imaginary quadratic fields of class number one.
Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.
We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.
We give a counting based proof of the Graham Pollak Theorem
The purpose of this article is to give a proof of the Orbifold Theorem announced by Thurston in late 1981: If $O$ is a compact, connected, orientable, irreducible and topologically atoroidal 3-orbifold with non-empty ramification locus,…
We prove a generalisation of the Grothendieck-Riemann-Roch theorem, which is valid for any proper and flat morphism between noetherian and separated schemes of odd characteristic.
Using a quadratic version of the Bott residue theorem, we give a quadratic refinement of the count of twisted cubic curves on hypersurfaces and complete intersections in a projective space.
We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that…
We prove that rigid representations of the fundamental group of a surface into the group of oreintation-preserving homeomorphisms of the circle are geometric, thereby establishing a converse statement of a theorem by the first author.
In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…
The Farkas lemma is proved and applied to obtain a structure theorem for polyhedra. These notes are based on a talk in the New York Number Theory Seminar on October, 20, 2022.
We give a new proof of Lucas' Theorem in elementary number theory.
We prove boundedness of rationally-connected threefolds in $\mathbb P^6$ under some extra-assumptions.
In this paper we prove a gap theorem for K\"ahler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for…
The Butterfly Theorem is explored in Taxicab Geometry.