剑桥英语语法369页关于定冠词the的使用原则之一刚好回答你这个问题。当名词属格作为限定词使用时，表示的是特指意义，即 Mr. Brown's daughter = the daughter of Mr. Brown.   Mary is Brown's daughter.这个句子并不意味着布郎先生只有一个女儿。

Under certain circumstances, however, the definite article can be appropriate with

a count singular even when the context does not strictly limit the number of entities

satisfying the description given in the nominal to just one:

[3] i Put your cup down on the arm of your chair.

ii He married the daughter of his bank manager.

An (arm-)chair has two arms, but the definite article in [i] is in order on the assumption

that it doesn’t matter which one you choose. Again, then, the definite article signals

my expectation that you don’t need to ask Which arm of my chair? In [ii] it could be

that the bank manager has in fact two daughters, but the is again appropriate on the

assumption that you don’t need to ask Which one?: perhaps the other is already married,

or too young to marry, perhaps you don’t know that there are two, and perhaps it simply

doesn’t matter, the important point being only that his bank manager was the father of

the woman he married.