There is certainly a degree in which nose beauty can vary from person to person or country to country.  However, for most people, a small, shark nose is seen as a sign of beauty.  There are several different operations which may achieve this affect.

Taking into account the current shape of  the nostrils and desired  outcome, the surgeon may resort to several methods. For example, cartilage, skin or fat may also be trimmed  and the nasal raised to create a naturally sharp nose, however, in certain cases cartilage may be inserted into the nose to strengthen and make it sharper.