William, in particular, had asked the couple's staff to convene the talks so that they could hear from a range of women, his office at Kensington Palace said.
He asked his staff for the opportunity "to hear directly from women working to support other women and girls.
"He also wanted to get a sense of work being done to help young women to achieve their full potential and for men to become more supportive of the women and girls in their lives."
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The couple met acid attack survivor Laxmi Agarwal and heard about her campaign against similar attacks.
Laxmi was attacked at age 15 by a 32-year-old man after she rejected his marriage proposal. She explained her decision to stop covering her face in order to encourage other victims not to hide and also spoke of her successful fight for tougher legal restrictions on the sale of acid. She is now a TV host, and director of the Chhanv Foundation, a charity dedicated to help survivors of acid attacks in India.
The couple also met with Sunita Jaiswal, a survivor of domestic abuse, who thanks to the support of the Azad Foundation, has turned her life around and has now provided a stable future for her daughters.
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Through the foundation Sunita was able to train as a driver, giving her independence and an income which allowed her to send her children to school.
The statement from the palace said she told the royal couple that the confidence she gained through training allowed her remaining fear "to flow out of her" and she now faces the future with optimism. She and Kate discussed the importance of mothers helping their daughters to develop strategies to become independent women.
They also met journalist Soumya Menon, who spoke about the role of media in these issues. She explained how the media can help women to tell their own stories.
Menon discussed her strong belief in continuing support and empowerment for women who are brave enough to speak up, so they are not abandoned and ignored after they have told their stories and the media have moved on.