Related papers: Proof of the orthogonal--Pin duality
For two non-congruent regular polygons of the same type, the method of finding the points in the plane at the equal distances to the vertices, is established. The existence of two points with this property is proved for two polygons with a…
In this article, we give proofs on the Arnold Lagrangian intersection conjecture on the cotangent bundles, Arnold-Givental Lagrangian intersection conjecture and the Arnold fixed point conjecture.
In this paper we have shown without assuming the four color theorem of planar graphs that every (bridgeless) cubic planar graph has a three-edge-coloring. This is an old-conjecture due to Tait in the squeal of efforts in settling the…
This paper has been withdrawn by the author due to a crucial error in last part of proof.
In this paper we show an index theorem for gerbes
In this article we prove the topological minimality of unions of several almost orthogonal planes of arbitrary dimensions. A particular case was proved in arXiv:1103.1468, where we proved the Almgren minimality (which is a weaker property…
By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form…
A proof is given of Rosenthal's \(\ell_1\) theorem.
This paper deals with the celebrated Euclidean theorem about isosceles triangles, comparing different proofs.
We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over $\mathbb{Z},$ and discuss alternatives to the Ozsv\'ath-Szab\'o $\tau$…
We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…
A proof of Sendov's conjecture is given.
We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for…
A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.
We consider quadrangles of perimeter $2$ in the plane with marked directed edge. To such quadrangle $Q$ a two-dimensional plane $\Pi\in\mathbb{R}^4$ with orthonormal base is corresponded. Orthogonal plane $\Pi^\bot$ defines a plane…
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
This paper proves a corner occupying theorem for the two-dimensional integral rectangle packing problem, stating that if it is possible to orthogonally place n arbitrarily given integral rectangles into an integral rectangular container…
We present a new view for duality in classical electromagnetic theory, based on the physical properties of a dual theory, eliminating the problems of the usual treatment of the subject.
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.
In this note, we provide a new proof that a $D$-connected graph $G$ on $n$ vertices has a general position orthogonal representation in $\RR^{n-D}$. Our argument, while based on many of the concepts from the original proof due to Lov\'asz,…