Related papers: Application of integral geometry to minimal surfac…
In this note, the correction to the proof of one theorem in some our previous paper [arXiv:1302.0589] will be given.
This supplementary part of the paper gr-qc 9312038 contains the necessary proofs of the claims stated in the main part.
This paper has been withdrawn because the new one gr-qc/0512095 includes all its results (as well as those in gr-qc/0511016) in a clearer way.
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
This note is the sequel of "Geometric structures as variational objects, I." It generalizes the main result and perspectives of that work to a class of geometric structures that includes integrable almost-complex structures.
This is an introductory survey written in Japanese on classical integrability from the viewpoint of symmetry reduction of 4-dimensional anti-self-dual Yang-Mills equations. Twistor construction methods are discussed in detail in…
These notes grew out of several introductory talks I gave during the years 2003--2005 on motivic integration. They give a short but thorough introduction to the flavor of motivic integration which nowadays goes by the name of geometric…
This paper is an updated version of a survey on projective configurations of subspaces in general position. The preceding version was published in Russian in 1989 and in English in 1990 (in Leningrad Math. J.) opening a new section ``Light…
We comment on the paper \"Uber Extremalprobleme der konformen Geometrie (On extremal problems in conformal geometry) by Teichm\"uller, published in 1941. This paper contains ideas on a wide generalization of his previous work on the…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in…
In these notes we discuss some relations between complex analysis (derivatives of Cauchy integrals) and curvatures of curves and surfaces. In higher dimensions the Cauchy integrals are based on generalizations of complex analysis using…
A very brief introduction to tropical and idempotent mathematics is presented. Applications to classical mechanics and geometry are especially examined.
These notes contain a brief introduction to the construction of toric Calabi--Yau hypersurfaces and complete intersections with a focus on issues relevant for string duality calculations. The last two sections can be read independently and…
This set of notes is intended for a short course aiming to provide an (almost) self-contained and (almost) elementary introduction to the topic of Information Geometry (IG) of the probability simplex. Such a course can be considered an…
It is a well known phenomenon that many classical minimal surfaces in Euclidean space also exist with higher dihedral symmetry. More precisely, these surfaces are solutions to free boundary problems in a wedge bounded by two vertical planes…
This paper contains corrections to Madea, Rosenberg, Torres-Ardila, "The Geometry of Loop Spaces II: Characteristic Classes," Advances in Math. (287), 2016, 485-518. The main change is that results about $\pi_1({\rm Diff}(M))$ are replaced…
We formulate a number of new results in Algebraic Geometry and outline their derivation from Theorem 2.12 which belongs to Algebraic Combinatorics.
In this paper, we study the geometry of surfaces with the generalised simple lift property. This work generalises previous results by Bernstein and Tinaglia, and it is motivated by the fact that leaves of a minimal lamination obtained as a…
This is a report of the author's talk at Kinosaki Algebraic Geometry Symposium 2018. We discuss some recent progress on the geometry of thin exceptional sets in Manin's Conjecture.