Matches in SemOpenAlex for { <https://semopenalex.org/work/W2965295890> ?p ?o ?g. }
Showing items 1 to 69 of
69
with 100 items per page.
- W2965295890 abstract "Let $mathcal{H}_0(mathbb{D})$ be the class of all analytic functions $f$ in the unit disc $mathbb{D} = {z in mathbb{C} : |z| 0$. Let $mathfrak{B} = { omega in mathcal{H}_0(mathbb{D}) : omega(mathbb{D}) subset mathbb{D}}$. We say that a one parameter family of analytic functions ${ f_t }_{t in I}$ in $mathcal{H}_0(mathbb{D})$ on an interval $I subset [-infty, infty]$, is a Loewner chain if $f_s$ is subordinate to $f_t$ whenever $s,t in I$ with $s<t$, i.e., there exists $omega_{s,t} in mathfrak{B}$ with $f_s = f_t circ omega_{s,t}$. Notice that we omit the univalence assumption on each $f_t$. We shall show that if $f_t'(0)$ is continuous and strictly increasing in $t$, then $f(z,t) := f_t(z)$ satisfies a partial differential equation which is a generalization of Loewner-Kufarev equation, and ${ f_t }_{t in I}$ can be expressed as $f_t = F circ g_t $, $t in I$, where $F$ is an analytic function on a disc $mathbb{D}(0,r) = { z in mathbb{C} : |z| < r }$ with $r = lim_{t uparrow sup I}f_t'(0) in (0, infty ]$ and $F(0)= F'(0)-1=0$, and ${ g_t }_{t in I}$ is a Loewner chain consists of univalent functions. In the second half we deals with Loewner chains ${ f_t }_{t in I}$ consists of universal covering maps which may be the most geometrically natural generalization of Loewner chains of univalent functions. For each $t in I$ let $C(f_t(mathbb{D}))$ be the connectivity of image domain of $f_t(mathbb{D})$. We shall show that if ${ f_t }_{tin I}$ is continuous, then the function $C(f_t(mathbb{D}))$ is nondecreasing and left continuous. Then we develop a Loewner theory on Fuchsian groups." @default.
- W2965295890 created "2019-08-13" @default.
- W2965295890 creator A5023393005 @default.
- W2965295890 date "2019-07-27" @default.
- W2965295890 modified "2023-09-27" @default.
- W2965295890 title "Lowener Theory on Analytic Universal Covering Maps" @default.
- W2965295890 cites W1481997517 @default.
- W2965295890 cites W1509839166 @default.
- W2965295890 cites W1518486998 @default.
- W2965295890 cites W1535866048 @default.
- W2965295890 cites W1552202016 @default.
- W2965295890 cites W1598995284 @default.
- W2965295890 cites W1996201279 @default.
- W2965295890 cites W2004020906 @default.
- W2965295890 cites W2015839991 @default.
- W2965295890 cites W2020271436 @default.
- W2965295890 cites W2037612300 @default.
- W2965295890 cites W2042379031 @default.
- W2965295890 cites W2050054420 @default.
- W2965295890 cites W2577918895 @default.
- W2965295890 cites W2798922842 @default.
- W2965295890 cites W2971015701 @default.
- W2965295890 hasPublicationYear "2019" @default.
- W2965295890 type Work @default.
- W2965295890 sameAs 2965295890 @default.
- W2965295890 citedByCount "0" @default.
- W2965295890 crossrefType "posted-content" @default.
- W2965295890 hasAuthorship W2965295890A5023393005 @default.
- W2965295890 hasConcept C114614502 @default.
- W2965295890 hasConcept C121332964 @default.
- W2965295890 hasConcept C122637931 @default.
- W2965295890 hasConcept C145420912 @default.
- W2965295890 hasConcept C2779557605 @default.
- W2965295890 hasConcept C33923547 @default.
- W2965295890 hasConcept C62520636 @default.
- W2965295890 hasConceptScore W2965295890C114614502 @default.
- W2965295890 hasConceptScore W2965295890C121332964 @default.
- W2965295890 hasConceptScore W2965295890C122637931 @default.
- W2965295890 hasConceptScore W2965295890C145420912 @default.
- W2965295890 hasConceptScore W2965295890C2779557605 @default.
- W2965295890 hasConceptScore W2965295890C33923547 @default.
- W2965295890 hasConceptScore W2965295890C62520636 @default.
- W2965295890 hasLocation W29652958901 @default.
- W2965295890 hasOpenAccess W2965295890 @default.
- W2965295890 hasPrimaryLocation W29652958901 @default.
- W2965295890 hasRelatedWork W1837994127 @default.
- W2965295890 hasRelatedWork W1997032408 @default.
- W2965295890 hasRelatedWork W2037026839 @default.
- W2965295890 hasRelatedWork W2037463727 @default.
- W2965295890 hasRelatedWork W2068851010 @default.
- W2965295890 hasRelatedWork W2113122494 @default.
- W2965295890 hasRelatedWork W2232674794 @default.
- W2965295890 hasRelatedWork W2331478133 @default.
- W2965295890 hasRelatedWork W2550248351 @default.
- W2965295890 hasRelatedWork W2804576509 @default.
- W2965295890 hasRelatedWork W2942387685 @default.
- W2965295890 hasRelatedWork W2945282941 @default.
- W2965295890 hasRelatedWork W2952306385 @default.
- W2965295890 hasRelatedWork W2986536460 @default.
- W2965295890 hasRelatedWork W2998106347 @default.
- W2965295890 hasRelatedWork W3014322938 @default.
- W2965295890 hasRelatedWork W3095862357 @default.
- W2965295890 hasRelatedWork W3171598163 @default.
- W2965295890 hasRelatedWork W3210509819 @default.
- W2965295890 hasRelatedWork W211664763 @default.
- W2965295890 isParatext "false" @default.
- W2965295890 isRetracted "false" @default.
- W2965295890 magId "2965295890" @default.
- W2965295890 workType "article" @default.