chhadmabhramanakshamata

ganitamadhye, adhik tantotantpane anek jatil chalanchya karyanchya siddhantat, seudoconvex sanch haah "aine"-aayami jatil avkash see "aine" madheel eka vishesh prakarcha khula sanch aahe. seudoconvex sanch mahatvache aahet, kaaran teey holomorphychya kshetranche vargikaran karnyas anumati detat. 
jaau dya. 
eka domain, mhanje eka open connected upasanch assa. sootra 2 varr jarr satat plurisufarmonic karya sootra _ 3 astitvat asel tarr sootra _ 2 heey 'seudoconvex' (kinwa 'hartog seudoconvex') aahe asey eka mhanato, jenekarun sanch 
sanch shabdant, serve vastavik sankhyanchya sutrasathi sootra _ 2 chaa tulanene sankshipt upasanch aahe, jarr sootra _ 2 madhye satat plurisuharmonic exotion function asel tarr domain heey seudoconvex aahe. pratyek (bhaumitikdrushtya) bahirmukh sanch haah seudoconvex asato. tathapi, ashee seudoconvex kshetre aahet jee bhaumitikdrushtya bahirmukh naheet.
jevha sootra _ 2 madhye sootra _ 10 (donada satat bhinn karnyayogya) seema asate, tevha hii kalpana levy seudoconvexitisarkhi asate, jyashi kaam karane sope asate. adhik visheshtah, sootra _ 10 simareshesaha, heey darshavile jaau shakate qee sootra _ 2 chey paribhashit karya aahe, i.eae., qee sootra 13 astitvat aahe jeey sootra 10 aahe jenekarun sootra 15, aanee sootra 16. aata, sootra 2 heey pratyek sutrasathi seudoconvex aay. eff. eff. aahe aanee sootra 19 heey pii. vareel jatil sparshikechya jaaget aahe, mhanje, 
vareel vyakhya vastavik vishleshanatil bahirmukhatechya vyakhyanshi samaan aahe.
jarr sootra _ 2 madhye sootra _ 10 seema nasel, tarr khaleel andaj parinam upayukt tharoo shakato. 
prastav 1 "jarr sootra _ 2 heey seudoconvex asel, tarr sootra _ 26 (gulgulit) simareshesaha, sootra _ 2 madhye tulanene sankshipt asalele, asey qee, '25' heey sootra baddh, jordarpane levy seudoconvex domain sootra astitvat aahe." 
yache kaaran asey qee ekada aaplyakade vyakhyepramane sootra _ 3 aale qee aapan pratyakshat eka "c" φ exotion function shodhu shakato.
prakaran "aine" = 1.
eka jatil parimanat, pratyek khule kshetra seudoconvex aahe. asha prakare seudoconvexitychi sankalpana 1 peksha jaast parimananmadhye adhik upayukt aahe.

