A Calabi – Yau manifold, also known as a Calabi – Yau space, is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics.

Some discrete quotients of the quintic by various Z < sub > 5 </ sub > actions are also Calabi – Yau and have received a lot of attention in the literature.

* Calabi – Yau Homepage is an interactive reference which describes many examples and classes of Calabi – Yau manifolds and also the physical theories in which they appear.

Mong Kok ( also spelt Mongkok ), is an area in the Yau Tsim Mong District on Kowloon Peninsula, Hong Kong.

* Temple Street ( 廟街, sometimes referred to as Men's Street ), extending into Jordan, is also in the area, however, the area famous for the Hong Kong specific goods are only in the section between Yau Ma Tei and Jordan.

Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling ( also in Guangdong ) in a family of eight children.

Yau also made a contribution in the case that the first Chern number c < sub > 1 </ sub > > 0, and conjectured its relation to the stability in the sense of geometric invariant theory in algebraic geometry.

* 16 Dec 1979: Waterloo and Argyle ( later renamed Yau Ma Tei and Mong Kok respectively ) stations opened, also as part of Kwun Tong Line.

Yau Ma Tei, also known as Waterloo ( see Name section ), is an area in the Yau Tsim Mong District in the south of the Kowloon Peninsula in Hong Kong.

It can also be spelt as Yaumatei, Yau Ma Ti, Yaumati or Yau-ma-Tee.

Tung Wah Group of Hospitals Museum in Kwong Wah Hospital details the history of Tung Wah Group of Hospitals and its relation with Hong Kong people, is also located in Yau Ma Tei.

* The Tin Hau temple in Yau Ma Tei is also famous in Hong Kong.

Yau Ma Tei is also accessible via Waterloo Road.

The new vacua described as F-theory were discovered by Vafa, and it also allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi – Yau four-folds.

* Calabi Yau manifolds admit a unique Einstein metric that is also Kähler.

He was also the Chairman of Henry Fok Estates Ltd and the Yau Wing Co of Hong Kong.

Retrieved on 2009-12-16 .</ ref > Meng also gave a less intricate constructive proof .< ref >< Meng, F. " Research into the Order 3 Magic Hexagon ", Shing-Tung Yau Awards, October 2008.

Next, it goes along the south shore of the Western New Territories, via Yau Kom Tau, Ting Kau, Sham Tseng, Tsing Lung Tau, Tai Lam, Siu Lam and So Kwun Wat and then reaches the Tuen Mun New Town, which was also known as Castle Peak ( after which the road was named ).

Yau proposed a series of conjectures when the manifold is non-compact, and made contributions towards their solutions.

“ Mobile M +: Yau Ma Tei ”, a contemporary art exhibition is the second program held by the Authority, which is the first in a series of pre-opening “ nomadic ” exhibition curated by M + before the completion of the museum building in 2017.

Ko Chun ( Chow Yun-Fat ) is now living a peaceful retirement on his French estate with his pregnant wife Wan Yau ( Sharla Cheung ), while his disciples Knife and Sing ( from the All For The Winner series ) have become world renowned in their own right.

In the twelfth month, he arrives in mainland China and gets into a series of comic misadventures with a small-time hustler named Little Trumpet ( Tony Leung Ka-Fai ), a police captain ( Elvis Tsui ), and Hoi Tong, a crime boss's daughter ( Chingmy Yau ).

* The slides used by Yau in a popular talk on the Poincaré conjecture.

* Waterloo Station or Yau Ma Tei ( MTR ), a station on the Hong Kong metro system

With Gary Horowitz, Philip Candelas and Andy Strominger Witten showed how string theory can lead to realistic descriptions by compactifying the theory on a higher dimensional manifold known as Calabi Yau manifolds.

* Some definitions put restrictions on the fundamental group of a Calabi – Yau manifold, such as demanding that it be finite or trivial.

Compactification on Calabi – Yau n-folds are important because they leave some of the original supersymmetry unbroken.

More precisely, in the absence of fluxes, compactification on a Calabi – Yau 3-fold ( real dimension 6 ) leaves one quarter of the original supersymmetry unbroken if the holonomy is the full SU ( 3 ).

A popular alternative known as large extra dimensions, which often occurs in braneworld models, is that the Calabi – Yau is large but we are confined to a small subset on which it intersects a D-brane.

F-theory compactifications on various Calabi – Yau four-folds provide physicists with a method to find a large number of classical solution in the so-called string theory landscape.

Yau Tsim Mong District (, Jyutping: jau4 zim1 wong6 keoi1 ) is one of 18 districts of Hong Kong, located on western Kowloon peninsula.

In algebraic geometry, the Calabi conjecture implies the Miyaoka – Yau inequality on Chern numbers of surfaces, a characterization of the complex projective plane and quotients of the two-dimensional complex unit ball, an important class of Shimura varieties.

Another important result of Donaldson – Uhlenbeck – Yau is that a holomorphic vector bundle is stable ( in the sense of David Mumford ) if and only if there exists an Hermitian – Yang – Mills metric on it.

Yau and Schoen continued their work on manifolds with positive scalar curvature, which led to Schoen's final solution of the Yamabe problem.

Yau and Karen Uhlenbeck proved the existence and uniqueness of Hermitian – Einstein metrics ( or equivalently Hermitian Yang – Mills connections ) for stable bundles on any compact Kähler manifold, extending an earlier result of Donaldson for projective algebraic surfaces, and M. S. Narasimhan and C. S. Seshadri for algebraic curves.

When Yau was working on his thesis about manifolds with non-positive curvature and their fundamental groups, he realized that it is possible to use harmonic maps to give alternative proofs of some results there.

One of Yau ’ s problems is about bounded harmonic functions, and harmonic functions on noncompact manifolds of polynomial growth.

Yau realized early in 1980s that the existence of special metrics on Kähler manifolds is equivalent to the stability of the manifolds.

After the door of China was opened to the west in the late 1970s, Yau revisited China in 1979 on the invitation of Hua Luogeng.

Yau is the director of all these three math institutes and visits them on a regular basis.

Because it travels under Victoria Harbour from Central and into the busy areas on Nathan Road ( Tsim Sha Tsui, Yau Ma Tei, and Mong Kok ) continuing into densely populated Sham Shui Po, it is a very heavily travelled line.

The Yau Ma Tei Typhoon Shelter became an exotic water area where restaurants on boats offered dishes of indigenous seafood.

A small portion of the Yau Ma Tei Fruit Market can be seen on the right.

Hoi Fu Court () is a mixed Home Ownership Scheme court and public estate built on reclaimed land of the old Yau Ma Tei Typhoon Shelter.

Yau Ma Tei is served by Tsuen Wan and Kwun Tong lines on the MTR metro system, at a single station with the same name, Yau Ma Tei MTR Station.