Related papers: A local Mazur-Ulam theorem
In this paper we prove a general theorem on the extensions of local nets which was inspired by recent examples of exotic extensions for Virasoro nets with central charge less than one and earlier work on cosets and conformal inclusions.…
Following the work of Jean-Loup Waldspurger, we prove the epsilon dichotomy part of the local Gross-Prasad conjecture over $\mathbb{R}$ for tempered local $L$-parameters.
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition,…
We give a constructive proof of the Carath\'eodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus.
We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.
We prove an improved form of an expectation of Polya and discuss several related questions
We derive a local uniform boundedness result for an elliptic equation having interior singularity.
We give a survey of recent developments in the investigation of the various local-global conjectures for representations of finite groups.
We prove a fixed point theorem for the action of certain local monodromy groups on \'etale covers and use it to deduce lower bounds in essential dimension. In particular, we give more geometric proofs of many (but not all) of the results of…
We prove Rubin's conjecture on the structure of local units in the anticyclotomic $\mathbb{Z}_p$-extension of unramified quadratic extension of $\mathbb{Q}_p$ in $p=3$ case by extending Burungale-Kobayashi-Ota's work.
We give a one-sentence proof of McLaughlin and Rundell's inverse uniqueness theorem.
We give an elementary proof to Hasse theorem.
We produce a new, shorter construction of a minor-universal planar graph.
We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.
We establish a structure theorem for the integral points on moduli of special linear rank two local systems over surfaces, using mapping class group descent and boundedness results for systoles of local systems.
In this article, we prove a rigidity theorem for isometric embeddings into the Schwarzschild manifold, by using the variational formula of quasi-local mass.
We prove relative versions of many earlier results about almost invariant sets and splittings of groups. In particular, we prove a relative version of the algebraic torus theorem, and we prove the existence and uniqueness of relative…
This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).
We prove a stability version of the Pr\'ekopa-Leindler inequality.