grammar - Definite articles before abstract nouns which don't relate to any (very) particular instances

I know that the title may be little misleading but here is the example which bothers me.

New approach to (the) ellipticity of linear differential operators

On contrary, I am sure that the following are correct

It follows from the ellipticity of the Laplace operator. (specified abstract noun)

Ellipticity is closely related to hyperbolicity. (just abstract nouns)

Similarly, I am not sure how to write the following sentence

I still believe in (the) kindness of people.

Where the following ones are obvious.

Kindness must be sustained. (specified abstract noun)

The kindness of John is beyond all norms. (just an abstract noun)

Thus, Here is my actual question eventually.

Question. Am I specifying abstract nouns in my examples and I should use "the" or is my specification artificial and I should omit "the"?

Answer

Though the use of one or more adjectives before an abstract noun does not make it specific, i.e., requiring a definite article, a prepositional or participial phrase after it does.

I am impressed by their unbounded kindness. [possessive pronoun, adjective]

I am impressed by the kindness of all my former students. [prepositional phrase]

I am impressed by the kindness shown to me after the accident. [participial phrase]