Related papers: Miquel-Steiner's point locus
We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the…
The aim of this note is to survey the results in some geometric problems related to the centroids and the static equilibrium points of convex bodies. In particular, we collect results related to Gr\"unbaum's inequality and the…
The three Apollonius circles of a triangle, each passing through a triangle vertex, the corresponding vertex of the cevian triangle of the incenter and the corresponding vertex of the circumcevian triangle of the symmedian point, are…
We observe that numerous symplectic resolutions can be expressed as intersections of twisted cotangent bundles. Additionally, their dual symplectic resolutions can be derived from intersections of dual twisted cotangent bundles. We…
We give a complete investigation of Morley's trisector theorem. If the intersections of the half lines starting from the adjacent vertices of a triangle form an equilateral triangle for an arbitrary triangle, then the half lines are the…
The purpose of this note is to clarify some details in McDuff and Segal's proof of the group-completion theorem and to generalize both this and the homology fibration criterion of McDuff to homology with twisted coefficients. This will be…
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. We consider extensions of the theorem and show that any convex polygon can be divided into parallel segments such…
To a topological groupoid endowed with an involution, we associate a topological groupoid of fixed points, generalizing the fixed-point subspace of a topological space with involution. We prove that when the topological groupoid with…
Coincident root loci are subvarieties of $S^d(C^2)$--the space of binary forms of degree $d$--labelled by partitions of $d$. Given a partition $\lambda$, let $X_\lambda$ be the set of forms with root multiplicity corresponding to $\lambda$.…
We exhibit two instances of the cyclic sieving phenomenon - one on dissections of a polygon of a fixed type and one on triangulations of a once-punctured polygon. We use these results to give refined enumerations of certain families of…
We classify the singular loci of real surfaces in three-space that contain two circles through each point. We characterize how a circle in such a surface meets this loci as it moves in its pencil and as such provide insight into the…
We add another brick to the large building comprising proofs of Pick's theorem. Although our proof is not the most elementary, it is short and reveals a connection between Pick's theorem and the pointwise convergence of multiple Fourier…
We develop a new approach to the study of the multipoint loci of holomorphic maps between complex manifolds. We relate the $k$-fold locus to the curvilinear component of the Hilbert scheme of $k$ points on the source space of the map, and…
In this paper, we determine all conformal Ricci collineations associated to the Levi-Civita connection on three-dimensional Lorentzian Lie groups .
Working over a field ${\mathbb{k}}$ of characteristic $\ne 2$, we study what we call bisector fields, which are arrangements of paired lines in the plane that have the property that each line in the arrangement crosses the paired lines in…
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…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
We investigate Steiner's Porism in finite Miquelian M\"obius planes constructed over the pair of finite fields $GF(p^m)$ and $GF(p^{2m})$, for $p$ an odd prime and $m \geq 1$. Properties of common tangent circles for two given concentric…
In a recent work Malkiewich and Merling proposed a definition of the equivariant $K$-theory of spaces for spaces equipped with an action of a finite group. We show that the fixed points of this spectrum admit a tom Dieck-type splitting. We…
These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone…