
unit disk

ganita saastramlo, "p" chuttoo unna open unit disk (ledhaa disk) (ikkada "p" anedi samatalamlo icchina binduvu), "p" nundi dhooram 1 kante takkuvagaa unna paayintla samitih
p" chuttoo unna closed unit disk anedi "p" nundi dhooram okati kante takkuvagaa ledhaa samanamga unde paayintla samitih
unit disclu anevi disclu mariyu unit bantula pratyeka sandarbhaalu; avi unit circle lopali bhaganni kaligi untaayi mariyu closed unit disk vishayamlo, unit sarkilnu kaligi untaayi.
marinni lakshanaalu lekunda, praamaanika euclidean metrikku sambandhinchi muulam gurinchi open unit disk, formula _ 3 kosam "unit disk" anae padaanni upayogistaaru. idhi muulam vadda kendrikrutamai unna vyaasaartham 1 gala vruttam lopali bhaagam. eee samitini okati kante takkuva sampoorna viluva kaligina anni sanklishta sankhyala samititoe gurtinchavacchu. sanklishta samatala (sii) yokka upasamitigaa chusinappudu, unit disknu tarachugaa suutram _ 4 gaa suuchistaaru.
open unit disk, plain mariyu eguva sagam plain.
function
open unit disk nundi plain varaku nijamaina vislaeshanhaatmaka mariyu bijective functionku idhi oka udaaharana; daani inverse function kooda vishlaeshanhaathmakamainadi. nijamaina 2-dimensional analytic manifoldga pariganinchabade open unit disk mottam plaenku isomorphicga untundi. mukhyamgaa, open unit disk mottam plain kii homomorphic gaa untundi.
ayithe open unit disk mariyu plain madhya conformal bijective mapp ledhu. reeman uparitalamgaa pariganinchabade open unit disk sanklishtamaina plain nundi bhinnamgaa untundi.
open unit disk mariyu open eguva sagam-plain madhya conformal bijective maplu unnaayi. kabatti reeman uparitalamgaa pariganinchabade open unit disk eguva sagam-plaenku isomorphic ("biholomorphic" ledhaa "conformally equivalent") gaa untundi, mariyu rendintinee tarachugaa parasparam maarchukoobadataayi.
marinta saadhaaranamgaa, reeman mapping siddhaantam sanklishtamaina plain nundi bhinnamgaa unde sanklishtamaina plain yokka prati saralamgaa anusandhaaninchabadina open subset open unit diskku conformal mariyu bijective myapnu angeekaristundani perkondi.
open unit disk nundi open eguva sagam-plain varaku oka bijective conformal mapp mobius parivartana.
rekhaaganitaparamgaa, nijamaina aksham vangi, kunchinchukupotundani oohinchavachhu, tadwara eguva sagam-plain disk lopali bhaagamgaa maarutundi mariyu nijamaina aksham disk yokka chuttukolatanu yerparustundi, eguvana oka binduvu kosam, "anantam vadda binduvu". open unit disk nundi open eguva sagam-plain varaku bijective conformal myapnu rendu stereographic projectionla kuurpugaa kooda nirminchavachuhu modata unit disknu stereographicga unit eguva sagam-golampai paiki project chestaaru, unit golam yokka "dakshina-dhruvam" nuu projection kendramgaa teesukuntaaru, aapai eee sagam-golam golamnu taakina niluvu sagam-samatalampai pakkaki project cheyabadutundi, sparsha binduvuku edurugaa sagam-golampai unna binduvunu projection kendramgaa teesukuntundi.
unit disk mariyu eguva sagam-plain hardy spacela kosam domainlugaa parasparam marchukolevu. eee vyatyaasaaniki dohadam chese vaastavam emitante, unit circle parimita (oka dimensional) lebsg kolatanu kaligi undagaa, nijamaina rekha kaadu.
hyperbolic plain.
open unit disk hyperbolic plain yokka paayinkaare disk modal kosam paayintla samitini yerparustundi. ekakam vruttaaniki lambamgaa unna vruttaakaara kaksyalu eee namoonaalo "rekhalanu" yerparustaayi. ekakam vruttam anedi kylie-clain metrik shaililo cross-nishpattini upayoginchadam dwara diskpy metriknu nirnayinche kylie sampoornam. avakalana jyaamiti bhaashalo, ekakam vruttaaniki lambamgaa unde vruttaakaara kaksyalu namuunaalooni binduvula madhya athi takkuva dooraanni choopinche bhougolikam. eee namoonaalo pratyeka ekaatmaka samuuham suu (1,1) dwara vyakteekarinchabadina kadalikalu untaayi. paina icchina mapping "g" dwara disk namuunaanu paayinkaare haaph-plain namoonaga maarchavacchu.
paayinkaare disk mariyu paayinkaare haaph-plain rendoo hyperbolic plain yokka "conformal" namuunaalu, antey chhedinche vakrarekhala madhya koonaalu vaati isometry samuuhaala kadalikala dwara samrakshinchabadataayi.
hyperbolic space yokka maroka namuunaa kooda open unit disk meeda nirminchabadindih beltramy-clain modal. idhi "conformal kaadu", conny geodesics sarala rekhalu anae lakshanaanni kaligi undhi.
itara kolamaanaalaku sambandhinchi unit disclu.
itara kolamaanaalaku sambandhinchi unit disclanu kooda pariganistaaru. udaaharanaku, taxi cab metrik mariyu chebishev metrik disclu chaturasraala laaga kanipistaayi (antarleena sthalaakruthi euclidean maadirigaane unnappatikee).
euclidean unit disk yokka vaisaalyam π mariyu daani chuttukolata 2π. dheeniki viruddhamgaa, taxicab jyaamitiloo unit disk yokka chuttukolata (taxicab metrikku sambandhinchi) 8.1932loe, stanisla golab oka pramaanam nundi utpannamayye kolamanalalo, unit disk yokka chuttukolata 6 mariyu 8 madhya edainaa viluvanu teesukogaladani, mariyu unit disk kramam tappakunda shatkonam ledhaa samaantara rekhaaganitamgaa untene eee teevra viluvalu pondabadatayani niroopinchaadu.

