Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An access theorem for analytic functions


Author: Marvin Ortel
Journal: Trans. Amer. Math. Soc. 347 (1995), 2213-2223
MSC: Primary 32C05; Secondary 31B05
MathSciNet review: 1273513
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that $ \mathcal{M}$ is an analytic manifold, $ {m_0} \in \mathcal{M},f:\mathcal{M} \to \mathbb{R}$, and $ f$ is analytic. Then at least one of the following three statements is true: (1) $ {m_0}$ is a local maximum of $ f$. (2) There is a continuous path $ \sigma :[0,1] \to \mathcal{M}$ such that $ \sigma (0) = {m_0}$, $ f \circ \sigma $ is strictly increasing on $ [0,1]$, and $ \sigma (1)$ is a local maximum of $ f$. (3) There is a continuous path $ \sigma :[0,1) \to \mathcal{M}$ with these properties: $ \sigma (0) = {m_0};f \circ \sigma $ is strictly increasing on $ [0,1)$; whenever $ K$ is a compact subset of $ \mathcal{M}$, there is a corresponding number $ d(K) \in [0,1)$ such that $ \sigma (t) \notin K$ for all $ t \in [d(K),1)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32C05, 31B05

Retrieve articles in all journals with MSC: 32C05, 31B05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1273513-3
PII: S 0002-9947(1995)1273513-3
Keywords: Real-analytic functions, analytic manifolds, singularities
Article copyright: © Copyright 1995 American Mathematical Society