Meaning of “under” - Learner’s Dictionary

under

preposition uk us /ˈʌndər/
BELOW

A1 below something:

She pushed her bag under the table.
The children were sitting under a tree.
BELOW THE SURFACE

A1 below the surface of something:

He could only keep his head under the water for a few seconds.
LESS THAN

A2 less than a number, amount, or age:

You can buy the whole system for just under $2000.
We don't serve alcohol to anyone under 18.
CONTROLLED BY

controlled or governed by a particular person, organization, etc:

The restaurant is under new management.
I'm managing the project and have three people under me.
RULE/LAW

according to a rule, law, etc:

Under the new law, all new buildings must be approved by the local government.
IN A PARTICULAR STATE

B2 in a particular state or condition:

The President is under pressure to resign.
Students are allowed to miss school under certain circumstances.
IN PROGRESS

B2 used to say that something is happening at the moment but is not finished:

A new 16-screen cinema is under construction.
Several different plans are under discussion.
NAME

using a particular name, especially one that is not your usual name:

He also wrote several detective novels under the name Edgar Sandys.
PLACE IN LIST

used to say which part of a list, book, library, etc you should look in to find something:

Books about health problems are under 'Medicine'.

(Definition of “under preposition” from the Cambridge Learner’s Dictionary © Cambridge University Press)