Don't quite agree with the other answers so I'll try and flesh out the differences.
First, it is important to understand that the cittamatra view is not the pinnacle of prajnaparamita. It is one stop that some beings need to arrive at before reaching the pinnacle of the perfection of wisdom.
Second, it is important to know that although the Laṅkāvatāra Sūtra is popularly said by some to be a sutra supporting cittamatra, actually it is quite critical of it. You can find in the sutra quite explicit admonitions that some of the concepts popular with cittamatra are actually upaya used by the Buddha out of compassion for those who are not ready to understand conceptually the perfection of wisdom and who are prone to fall to annihilation or extreme fear as they approach the truth.
With those points made I want you to look at the third point in the verse sighted which has been overlooked.
The Blessed One replied: There are four things by the fulfilling of
which an earnest disciple may gain self-realization of Noble Wisdom
and become and Bodhisattva-Mahasattva: First, he must have a clear
understanding that all things are only manifestations of the mind
itself; second, he must discard the notion of birth, abiding and
disappearance; third, he must clearly understand the ego-less-ness of
both things and persons; and fourth, he must have a true conception of
what constitutes self-realization of Noble Wisdom, provided with these
four understandings, earnest disciples may become Bodhisattvas and
attain Transcendental Intelligence.
Now look at the formulation of your question with emphasis on the third point above.
If everything is my own mind, what about other peoples minds? Are they
also my own mind?
No, they are not your own mind. Your own mind is not your own mind. Because 'you' do not exist in the way that 'you' think you do.
What you are doing with your question is diving up the world into two; a duality if you will. On one side you have you and your mind. Set aside for a second the question of what 'you' are given that all things are manifestation of mind. On the other side you have the rest of the world and you interpret what the Buddha has said as putting you and your mind as masters of this world. You've interpreted it to say that only you and your own mind are real and all the rest is just a fiction that your mind is making up.
This is just not even close to what the Buddha was saying. Ask yourself... if all things are manifestation of the mind itself (note: not 'your' mind), then what of the mind itself? Is it also a manifestation of mind? Is the Buddha saying that only the mind is real? If only the mind is real, then there can be no thing, no separate non-mind thing, that is the 'owner' of that mind, right? So what does that make 'you'?
Let's just say hypothetically that the mind is real and the only thing that is real. So how do you interpret the third point above? The Buddha in the very same passage is telling us that all people and phenomena are empty. That neither people nor phenomena contain any inherent being. How can you square that with this idea of 'your' mind or even with the idea that 'mind' itself is real?
To truly understand these four points and what the Buddha is after in this passage you have to understand emptiness and what is meant by this third point. It is the teaching on emptiness and anatta that is unique and clears up any and all doubt that the Buddha was referring to some form of solipsism when teaching that all should be regarded as manifestation of mind. Mind itself is empty of any inherent being. Mind itself is not real.
I'm hopeful this is helpful, but if you find yourself just confused by this I'd suggest putting it down and focusing on the method aspects of the path.