Shiu-Yuen Cheng

Shiu-Yuen Cheng

ɓii aadama

Jinsu	gorko
Ɓii-leydiyankaaku	Ciina
Innde ɓesngu	Zheng
Ɗuubi daygo	20. century
Ɗoforde	Hong Kong
Wolde	Chinese, Inngilisjo
Sana'aji	mathematician, jannginoowo, university teacher
Field of work	differential geometry, partial differential equation, game theory
Employer	Hong Kong University of Science and Technology, University of California, Los Angeles, The Chinese University of Hong Kong, Tsinghua University
Janngi to	The Chinese University of Hong Kong, University of California, Berkeley, Pui Ching Middle School
Doctoral advisor	Shiing-Shen Chern
Memba en	American Mathematical Society
Award received	Fellow of the American Mathematical Society
Academic appointment	UCLA Department of Mathematics, Yau Mathematical Sciences Center, Tsinghua University

Shiu-Yuen Cheng (鄭紹遠) ko ganndo hiisiwal to Hong Kong. O wonii hannde hooreejo porfeseer hiisa to duɗal jaaɓi haaɗtirde ganndal e karallaagal to Hong Kong. Cheng heɓi doktoraa mum Ph.D. e hitaande 1974, e gardagol Shiing-Shen Chern, ummoriiɗo to duɗal jaaɓi haaɗtirde Kaliforni to Berkeley.Ndeen Cheng waɗii duuɓi seeɗa e golle makko caggal doktoraa e balloowo jannginoowo to duɗal jaaɓi haaɗtirde Princeton e duɗal jaaɓi haaɗtirde dowla New York to Stony Brook. Ndeen o wonti porfeseer timmuɗo to duɗal jaaɓi haaɗtirde Kaliforni to Los Angeles. Cheng ardii departemaaji Hiisawal to Duɗal Jaaɓihaaɗtirde Siin to Hong Kong e Duɗal Jaaɓihaaɗtirde Ganndal e Karallaagal Hong Kong e kitaale 1990. E hitaande 2004, o wonti Deenoowo ganndal to HKUST. E hitaande 2012, o wonti tergal fedde hiisawal Amerik.

O anndaama no feewi e darnde makko e joometiri feere-feere e pottitte feere-feere feccere, ina jeyaa heen miijo nannditgol eigenvalue Cheng, miijo Cheng jowitiingo e njaajeendi ɓurndi mawnude, e golle keewɗe e Shing-Tung Yau . Golle Cheng e Yau keewɗe ina njeyaa e korpus golle ɗe Yau rokkaa njeenaari Fields e hitaande 1982. Gila hitaande 2020, golle wiɗto Cheng ɓurɗe ɓadaade ɗee njaltinaa ko e hitaande 1996.

Darnde karallaagal

Estimaaji gradient e kuutoragol mum en

E hitaande 1975, Shing-Tung Yau heɓi limngal kesal ngam saabaade pottitte ceertuɗe elliptik gonɗe e doggol ɗiɗaɓol e dow won e mbaydiiji Riemannian timmuɗi. Cheng e Yau mbaawii ƴellitde limto Yau ngoo e huutoraade feere nde Eugenio Calabi ƴetti . [CY75] Njiylawu oo, anndiraango limto mbaylaandi Cheng–Yau, ina tawee e kala nokku e fannu ƴeewndo joometiri . Ko ɗum waɗi, Cheng e Yau mbaawii hollirde woodde gollal keeringal, nanndungal e teddeendi keeringal gadanal, golloowo Laplace-Beltrami e dow manifolde Riemannian timmunde.

Cheng e Yau kuutoriima ngool laawol ngam faamde hipersurfaaji nannduɗi e weeyo Minkowski e joometiri hipersurfaaji e nder weeyo affine . [CY76a] [CY86] Kuutoragol keeringol njeñtudi maɓɓe ko teskuyaaji Bernstein wonande hipersurfaaji nannduɗi e weeyo udditiiɗi e weeyo Minkowski mo njuuteendi mum woni no feewi ; kala hipersurface hono noon ina foti wonde dingiral. [CY76a]

Nder hitaande 1916, Hermann Weyl heɓti anndal feere-feere ngam dogginki joometiri dow ko laaɓi nder weeyo Euclidean. E huutoraade doosgal ɓurngal mawnude, o waawii jogaade doole joometiri yaajndi to bannge joometiri ndernderi. Cheng e Yau kuutoriima ɗum e ngonka hipersurfaaji e nder mbaydiiji Riemannian. [CY77b]

Caɗeele Minkowski e pottital Monge-Ampère

Kala hipersurface udditirɗo no feewi e nder weeyo Euclidean ℝn + 1 ina waawi siforeede no mbaydi n -dimensionnel sfera, rewrude e kartal Gauss . Caɗeele Minkowski ina naamnoo so tawii gollal ɓuuɓngal e moƴƴal gonngal e dow tagofeere n -dimensionnel ina waawi feeñde no ɓuuɓol skalaar ngol metrik Riemann ngol ngalɗoo nanondiral addani. Ɗumɗoon noon, ko Louis Nirenberg, ƴetti ɗum e hitaande 1953, e nder haala ka n foti ko e ɗiɗi. E hitaande 1976, Cheng e Yau ndartini caɗeele ɗee e kuuɓal. [CY76b]

E kuutoragol waylo-waylo Legendre, kuutorɗe pottital Monge-Ampère ina ndokka kadi hipersurfaaji ɓuuɓɗi e weeyo Euclide ; ɓuuɓol skalaar ngol metrik ndernderiijo ngol ko bannge ñaamo pottital Monge-Ampère ngal yamiri. Ko noon ne kadi, Cheng e Yau mbaawi huutoraade ƴeewndo mum en caɗeele Minkowski ngam heɓde humpitooji ko faati e ƴeewndo pottitte Monge-Ampère. [CY77a] Ko ɗum kuutorgal keeringal, ɓe keɓii miijo gonngo e keertinagol kuuɓtodinngo adanngo wonande caɗeele keeri-nafoore wonande pottital Monge-Ampère. Luis Caffarelli, Nirenberg e Joel Spruck caggal ɗuum ƴettii laabi ɓurɗi yooɗde ngam haɓaade ngool caɗeele.